Results of Bessel Functions
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 10.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{2}\deriv[2]{w}{z}+z\deriv{w}{z}+(z^{2}-\nu^{2})w = 0} | (z)^(2)* diff(w, [z$(2)])+ z*diff(w, z)+((z)^(2)- (nu)^(2))* w = 0 |
(z)^(2)* D[w, {z, 2}]+ z*D[w, z]+((z)^(2)- (\[Nu])^(2))* w = 0 |
Failure | Failure | Fail 11.31370849-11.31370849*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}11.31370849-11.31370849*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-11.31370849-11.31370849*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-11.31370849-11.31370849*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-11.313708498984761, 11.313708498984761] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-11.313708498984761, 11.313708498984761] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[11.313708498984761, -11.313708498984761] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[11.313708498984761, -11.313708498984761] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = (\tfrac{1}{2}z)^{\nu}\sum_{k=0}^{\infty}(-1)^{k}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}}} | BesselJ(nu, z)=((1)/(2)*z)^(nu)* sum((- 1)^(k)*(((1)/(4)*(z)^(2))^(k))/(factorial(k)*GAMMA(nu + k + 1)), k = 0..infinity) |
BesselJ[\[Nu], z]=(Divide[1,2]*z)^(\[Nu])* Sum[(- 1)^(k)*Divide[(Divide[1,4]*(z)^(2))^(k),(k)!*Gamma[\[Nu]+ k + 1]], {k, 0, Infinity}] |
Successful | Successful | - | - |
| 10.2.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = \frac{\BesselJ{\nu}@{z}\cos@{\nu\pi}-\BesselJ{-\nu}@{z}}{\sin@{\nu\pi}}} | BesselY(nu, z)=(BesselJ(nu, z)*cos(nu*Pi)- BesselJ(- nu, z))/(sin(nu*Pi)) |
BesselY[\[Nu], z]=Divide[BesselJ[\[Nu], z]*Cos[\[Nu]*Pi]- BesselJ[- \[Nu], z],Sin[\[Nu]*Pi]] |
Successful | Successful | - | - |
| 10.4#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{-n}@{z} = (-1)^{n}\BesselJ{n}@{z}} | BesselJ(- n, z)=(- 1)^(n)* BesselJ(n, z) |
BesselJ[- n, z]=(- 1)^(n)* BesselJ[n, z] |
Failure | Failure | Successful | Successful |
| 10.4#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{-n}@{z} = (-1)^{n}\BesselY{n}@{z}} | BesselY(- n, z)=(- 1)^(n)* BesselY(n, z) |
BesselY[- n, z]=(- 1)^(n)* BesselY[n, z] |
Failure | Failure | Successful | Successful |
| 10.4#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{-n}@{z} = (-1)^{n}\HankelH{1}{n}@{z}} | HankelH1(- n, z)=(- 1)^(n)* HankelH1(n, z) |
HankelH1[- n, z]=(- 1)^(n)* HankelH1[n, z] |
Successful | Failure | - | Successful |
| 10.4#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{-n}@{z} = (-1)^{n}\HankelH{2}{n}@{z}} | HankelH2(- n, z)=(- 1)^(n)* HankelH2(n, z) |
HankelH2[- n, z]=(- 1)^(n)* HankelH2[n, z] |
Failure | Failure | Successful | Successful |
| 10.4#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = \BesselJ{\nu}@{z}+i\BesselY{\nu}@{z}} | HankelH1(nu, z)= BesselJ(nu, z)+ I*BesselY(nu, z) |
HankelH1[\[Nu], z]= BesselJ[\[Nu], z]+ I*BesselY[\[Nu], z] |
Failure | Successful | Successful | - |
| 10.4#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = \BesselJ{\nu}@{z}-i\BesselY{\nu}@{z}} | HankelH2(nu, z)= BesselJ(nu, z)- I*BesselY(nu, z) |
HankelH2[\[Nu], z]= BesselJ[\[Nu], z]- I*BesselY[\[Nu], z] |
Failure | Successful | Successful | - |
| 10.4#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{1}{2}\left(\HankelH{1}{\nu}@{z}+\HankelH{2}{\nu}@{z}\right)} | BesselJ(nu, z)=(1)/(2)*(HankelH1(nu, z)+ HankelH2(nu, z)) |
BesselJ[\[Nu], z]=Divide[1,2]*(HankelH1[\[Nu], z]+ HankelH2[\[Nu], z]) |
Successful | Successful | - | - |
| 10.4#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = \frac{1}{2i}\left(\HankelH{1}{\nu}@{z}-\HankelH{2}{\nu}@{z}\right)} | BesselY(nu, z)=(1)/(2*I)*(HankelH1(nu, z)- HankelH2(nu, z)) |
BesselY[\[Nu], z]=Divide[1,2*I]*(HankelH1[\[Nu], z]- HankelH2[\[Nu], z]) |
Successful | Successful | - | - |
| 10.4.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \csc@{\nu\pi}\left(\BesselY{-\nu}@{z}-\BesselY{\nu}@{z}\cos@{\nu\pi}\right)} | BesselJ(nu, z)= csc(nu*Pi)*(BesselY(- nu, z)- BesselY(nu, z)*cos(nu*Pi)) |
BesselJ[\[Nu], z]= Csc[\[Nu]*Pi]*(BesselY[- \[Nu], z]- BesselY[\[Nu], z]*Cos[\[Nu]*Pi]) |
Successful | Successful | - | - |
| 10.4#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{-\nu}@{z} = e^{\nu\pi i}\HankelH{1}{\nu}@{z}} | HankelH1(- nu, z)= exp(nu*Pi*I)*HankelH1(nu, z) |
HankelH1[- \[Nu], z]= Exp[\[Nu]*Pi*I]*HankelH1[\[Nu], z] |
Successful | Failure | - | Successful |
| 10.4#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{-\nu}@{z} = e^{-\nu\pi i}\HankelH{2}{\nu}@{z}} | HankelH2(- nu, z)= exp(- nu*Pi*I)*HankelH2(nu, z) |
HankelH2[- \[Nu], z]= Exp[- \[Nu]*Pi*I]*HankelH2[\[Nu], z] |
Successful | Failure | - | Successful |
| 10.4.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = i\csc@{\nu\pi}\left(e^{-\nu\pi i}\BesselJ{\nu}@{z}-\BesselJ{-\nu}@{z}\right)} | HankelH1(nu, z)= I*csc(nu*Pi)*(exp(- nu*Pi*I)*BesselJ(nu, z)- BesselJ(- nu, z)) |
HankelH1[\[Nu], z]= I*Csc[\[Nu]*Pi]*(Exp[- \[Nu]*Pi*I]*BesselJ[\[Nu], z]- BesselJ[- \[Nu], z]) |
Successful | Successful | - | - |
| 10.4.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle i\csc@{\nu\pi}\left(e^{-\nu\pi i}\BesselJ{\nu}@{z}-\BesselJ{-\nu}@{z}\right) = \csc@{\nu\pi}\left(\BesselY{-\nu}@{z}-e^{-\nu\pi i}\BesselY{\nu}@{z}\right)} | I*csc(nu*Pi)*(exp(- nu*Pi*I)*BesselJ(nu, z)- BesselJ(- nu, z))= csc(nu*Pi)*(BesselY(- nu, z)- exp(- nu*Pi*I)*BesselY(nu, z)) |
I*Csc[\[Nu]*Pi]*(Exp[- \[Nu]*Pi*I]*BesselJ[\[Nu], z]- BesselJ[- \[Nu], z])= Csc[\[Nu]*Pi]*(BesselY[- \[Nu], z]- Exp[- \[Nu]*Pi*I]*BesselY[\[Nu], z]) |
Failure | Successful | Successful | - |
| 10.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = i\csc@{\nu\pi}\left(\BesselJ{-\nu}@{z}-e^{\nu\pi i}\BesselJ{\nu}@{z}\right)} | HankelH2(nu, z)= I*csc(nu*Pi)*(BesselJ(- nu, z)- exp(nu*Pi*I)*BesselJ(nu, z)) |
HankelH2[\[Nu], z]= I*Csc[\[Nu]*Pi]*(BesselJ[- \[Nu], z]- Exp[\[Nu]*Pi*I]*BesselJ[\[Nu], z]) |
Successful | Successful | - | - |
| 10.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle i\csc@{\nu\pi}\left(\BesselJ{-\nu}@{z}-e^{\nu\pi i}\BesselJ{\nu}@{z}\right) = \csc@{\nu\pi}\left(\BesselY{-\nu}@{z}-e^{\nu\pi i}\BesselY{\nu}@{z}\right)} | I*csc(nu*Pi)*(BesselJ(- nu, z)- exp(nu*Pi*I)*BesselJ(nu, z))= csc(nu*Pi)*(BesselY(- nu, z)- exp(nu*Pi*I)*BesselY(nu, z)) |
I*Csc[\[Nu]*Pi]*(BesselJ[- \[Nu], z]- Exp[\[Nu]*Pi*I]*BesselJ[\[Nu], z])= Csc[\[Nu]*Pi]*(BesselY[- \[Nu], z]- Exp[\[Nu]*Pi*I]*BesselY[\[Nu], z]) |
Failure | Successful | Successful | - |
| 10.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\BesselJ{\nu}@{z},\BesselJ{-\nu}@{z}} = \BesselJ{\nu+1}@{z}\BesselJ{-\nu}@{z}+\BesselJ{\nu}@{z}\BesselJ{-\nu-1}@{z}} | (BesselJ(nu, z))*diff(BesselJ(- nu, z), z)-diff(BesselJ(nu, z), z)*(BesselJ(- nu, z))= BesselJ(nu + 1, z)*BesselJ(- nu, z)+ BesselJ(nu, z)*BesselJ(- nu - 1, z) |
Wronskian[{BesselJ[\[Nu], z], BesselJ[- \[Nu], z]}, z]= BesselJ[\[Nu]+ 1, z]*BesselJ[- \[Nu], z]+ BesselJ[\[Nu], z]*BesselJ[- \[Nu]- 1, z] |
Successful | Successful | - | - |
| 10.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu+1}@{z}\BesselJ{-\nu}@{z}+\BesselJ{\nu}@{z}\BesselJ{-\nu-1}@{z} = -2\sin@{\nu\pi}/(\pi z)} | BesselJ(nu + 1, z)*BesselJ(- nu, z)+ BesselJ(nu, z)*BesselJ(- nu - 1, z)= - 2*sin(nu*Pi)/(Pi*z) |
BesselJ[\[Nu]+ 1, z]*BesselJ[- \[Nu], z]+ BesselJ[\[Nu], z]*BesselJ[- \[Nu]- 1, z]= - 2*Sin[\[Nu]*Pi]/(Pi*z) |
Failure | Successful | Successful | - |
| 10.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\BesselJ{\nu}@{z},\BesselY{\nu}@{z}} = \BesselJ{\nu+1}@{z}\BesselY{\nu}@{z}-\BesselJ{\nu}@{z}\BesselY{\nu+1}@{z}} | (BesselJ(nu, z))*diff(BesselY(nu, z), z)-diff(BesselJ(nu, z), z)*(BesselY(nu, z))= BesselJ(nu + 1, z)*BesselY(nu, z)- BesselJ(nu, z)*BesselY(nu + 1, z) |
Wronskian[{BesselJ[\[Nu], z], BesselY[\[Nu], z]}, z]= BesselJ[\[Nu]+ 1, z]*BesselY[\[Nu], z]- BesselJ[\[Nu], z]*BesselY[\[Nu]+ 1, z] |
Successful | Successful | - | - |
| 10.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu+1}@{z}\BesselY{\nu}@{z}-\BesselJ{\nu}@{z}\BesselY{\nu+1}@{z} = 2/(\pi z)} | BesselJ(nu + 1, z)*BesselY(nu, z)- BesselJ(nu, z)*BesselY(nu + 1, z)= 2/(Pi*z) |
BesselJ[\[Nu]+ 1, z]*BesselY[\[Nu], z]- BesselJ[\[Nu], z]*BesselY[\[Nu]+ 1, z]= 2/(Pi*z) |
Failure | Successful | Successful | - |
| 10.5.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu+1}@{z}\HankelH{1}{\nu}@{z}-\BesselJ{\nu}@{z}\HankelH{1}{\nu+1}@{z} = 2i/(\pi z)} | BesselJ(nu + 1, z)*HankelH1(nu, z)- BesselJ(nu, z)*HankelH1(nu + 1, z)= 2*I/(Pi*z) |
BesselJ[\[Nu]+ 1, z]*HankelH1[\[Nu], z]- BesselJ[\[Nu], z]*HankelH1[\[Nu]+ 1, z]= 2*I/(Pi*z) |
Failure | Successful | Successful | - |
| 10.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu+1}@{z}\HankelH{2}{\nu}@{z}-\BesselJ{\nu}@{z}\HankelH{2}{\nu+1}@{z} = -2i/(\pi z)} | BesselJ(nu + 1, z)*HankelH2(nu, z)- BesselJ(nu, z)*HankelH2(nu + 1, z)= - 2*I/(Pi*z) |
BesselJ[\[Nu]+ 1, z]*HankelH2[\[Nu], z]- BesselJ[\[Nu], z]*HankelH2[\[Nu]+ 1, z]= - 2*I/(Pi*z) |
Failure | Successful | Successful | - |
| 10.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\HankelH{1}{\nu}@{z},\HankelH{2}{\nu}@{z}} = \HankelH{1}{\nu+1}@{z}\HankelH{2}{\nu}@{z}-\HankelH{1}{\nu}@{z}\HankelH{2}{\nu+1}@{z}} | (HankelH1(nu, z))*diff(HankelH2(nu, z), z)-diff(HankelH1(nu, z), z)*(HankelH2(nu, z))= HankelH1(nu + 1, z)*HankelH2(nu, z)- HankelH1(nu, z)*HankelH2(nu + 1, z) |
Wronskian[{HankelH1[\[Nu], z], HankelH2[\[Nu], z]}, z]= HankelH1[\[Nu]+ 1, z]*HankelH2[\[Nu], z]- HankelH1[\[Nu], z]*HankelH2[\[Nu]+ 1, z] |
Successful | Successful | - | - |
| 10.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu+1}@{z}\HankelH{2}{\nu}@{z}-\HankelH{1}{\nu}@{z}\HankelH{2}{\nu+1}@{z} = -4i/(\pi z)} | HankelH1(nu + 1, z)*HankelH2(nu, z)- HankelH1(nu, z)*HankelH2(nu + 1, z)= - 4*I/(Pi*z) |
HankelH1[\[Nu]+ 1, z]*HankelH2[\[Nu], z]- HankelH1[\[Nu], z]*HankelH2[\[Nu]+ 1, z]= - 4*I/(Pi*z) |
Failure | Successful | Successful | - |
| 10.6#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{\nu} = \BesselJ{\nu}@{a}\BesselY{\nu}@{b}-\BesselJ{\nu}@{b}\BesselY{\nu}@{a}} | p[nu]= BesselJ(nu, a)*BesselY(nu, b)- BesselJ(nu, b)*BesselY(nu, a) |
Subscript[p, \[Nu]]= BesselJ[\[Nu], a]*BesselY[\[Nu], b]- BesselJ[\[Nu], b]*BesselY[\[Nu], a] |
Failure | Failure | Fail 1.414213562+1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), p[nu] = 2^(1/2)+I*2^(1/2)}1.414213562-1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), p[nu] = 2^(1/2)-I*2^(1/2)}-1.414213562-1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), p[nu] = -2^(1/2)-I*2^(1/2)}-1.414213562+1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), p[nu] = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Skip |
| 10.6#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{\nu} = \BesselJ{\nu}@{a}\BesselY{\nu}'@{b}-\BesselJ{\nu}'@{b}\BesselY{\nu}@{a}} | q[nu]= BesselJ(nu, a)*subs( temp=b, diff( BesselY(nu, temp), temp$(1) ) )- subs( temp=b, diff( BesselJ(nu, temp), temp$(1) ) )*BesselY(nu, a) |
Subscript[q, \[Nu]]= BesselJ[\[Nu], a]*(D[BesselY[\[Nu], temp], {temp, 1}]/.temp-> b)- (D[BesselJ[\[Nu], temp], {temp, 1}]/.temp-> b)*BesselY[\[Nu], a] |
Failure | Failure | Fail 1.189134483+1.639292641*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), q[nu] = 2^(1/2)+I*2^(1/2)}1.189134483-1.189134483*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), q[nu] = 2^(1/2)-I*2^(1/2)}-1.639292641-1.189134483*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), q[nu] = -2^(1/2)-I*2^(1/2)}-1.639292641+1.639292641*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), q[nu] = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Skip |
| 10.6#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r_{\nu} = \BesselJ{\nu}'@{a}\BesselY{\nu}@{b}-\BesselJ{\nu}@{b}\BesselY{\nu}'@{a}} | r[nu]= subs( temp=a, diff( BesselJ(nu, temp), temp$(1) ) )*BesselY(nu, b)- BesselJ(nu, b)*subs( temp=a, diff( BesselY(nu, temp), temp$(1) ) ) |
Subscript[r, \[Nu]]= (D[BesselJ[\[Nu], temp], {temp, 1}]/.temp-> a)*BesselY[\[Nu], b]- BesselJ[\[Nu], b]*(D[BesselY[\[Nu], temp], {temp, 1}]/.temp-> a) |
Failure | Failure | Fail 1.639292641+1.189134483*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), r[nu] = 2^(1/2)+I*2^(1/2)}1.639292641-1.639292641*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), r[nu] = 2^(1/2)-I*2^(1/2)}-1.189134483-1.639292641*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), r[nu] = -2^(1/2)-I*2^(1/2)}-1.189134483+1.189134483*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), r[nu] = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Skip |
| 10.6#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{\nu} = \BesselJ{\nu}'@{a}\BesselY{\nu}'@{b}-\BesselJ{\nu}'@{b}\BesselY{\nu}'@{a}} | s[nu]= subs( temp=a, diff( BesselJ(nu, temp), temp$(1) ) )*subs( temp=b, diff( BesselY(nu, temp), temp$(1) ) )- subs( temp=b, diff( BesselJ(nu, temp), temp$(1) ) )*subs( temp=a, diff( BesselY(nu, temp), temp$(1) ) ) |
Subscript[s, \[Nu]]= (D[BesselJ[\[Nu], temp], {temp, 1}]/.temp-> a)*(D[BesselY[\[Nu], temp], {temp, 1}]/.temp-> b)- (D[BesselJ[\[Nu], temp], {temp, 1}]/.temp-> b)*(D[BesselY[\[Nu], temp], {temp, 1}]/.temp-> a) |
Failure | Failure | Fail 1.414213562+1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), s[nu] = 2^(1/2)+I*2^(1/2)}1.414213562-1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), s[nu] = 2^(1/2)-I*2^(1/2)}-1.414213562-1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), s[nu] = -2^(1/2)-I*2^(1/2)}-1.414213562+1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), s[nu] = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Skip |
| 10.8.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{n}@{z} = -\frac{(\tfrac{1}{2}z)^{-n}}{\pi}\sum_{k=0}^{n-1}\frac{(n-k-1)!}{k!}\left(\tfrac{1}{4}z^{2}\right)^{k}+\frac{2}{\pi}\ln@{\tfrac{1}{2}z}\BesselJ{n}@{z}-\frac{(\tfrac{1}{2}z)^{n}}{\pi}\sum_{k=0}^{\infty}(\digamma@{k+1}+\digamma@{n+k+1})\frac{(-\tfrac{1}{4}z^{2})^{k}}{k!(n+k)!}} | BesselY(n, z)= -(((1)/(2)*z)^(- n))/(Pi)*sum((factorial(n - k - 1))/(factorial(k))*((1)/(4)*(z)^(2))^(k), k = 0..n - 1)+(2)/(Pi)*ln((1)/(2)*z)*BesselJ(n, z)-(((1)/(2)*z)^(n))/(Pi)*sum((Psi(k + 1)+ Psi(n + k + 1))*((-(1)/(4)*(z)^(2))^(k))/(factorial(k)*factorial(n + k)), k = 0..infinity) |
BesselY[n, z]= -Divide[(Divide[1,2]*z)^(- n),Pi]*Sum[Divide[(n - k - 1)!,(k)!]*(Divide[1,4]*(z)^(2))^(k), {k, 0, n - 1}]+Divide[2,Pi]*Log[Divide[1,2]*z]*BesselJ[n, z]-Divide[(Divide[1,2]*z)^(n),Pi]*Sum[(PolyGamma[k + 1]+ PolyGamma[n + k + 1])*Divide[(-Divide[1,4]*(z)^(2))^(k),(k)!*(n + k)!], {k, 0, Infinity}] |
Error | Failure | - | Successful |
| 10.9.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}}\diff{\theta}} | BesselJ(0, z)=(1)/(Pi)*int(cos(z*sin(theta)), theta = 0..Pi) |
BesselJ[0, z]=Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]], {\[Theta], 0, Pi}] |
Successful | Failure | - | Successful |
| 10.9.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}\diff{\theta}} | (1)/(Pi)*int(cos(z*sin(theta)), theta = 0..Pi)=(1)/(Pi)*int(cos(z*cos(theta)), theta = 0..Pi) |
Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]], {\[Theta], 0, Pi}]=Divide[1,Pi]*Integrate[Cos[z*Cos[\[Theta]]], {\[Theta], 0, Pi}] |
Successful | Failure | - | Successful |
| 10.9.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{n}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}-n\theta}\diff{\theta}} | BesselJ(n, z)=(1)/(Pi)*int(cos(z*sin(theta)- n*theta), theta = 0..Pi) |
BesselJ[n, z]=Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]- n*\[Theta]], {\[Theta], 0, Pi}] |
Failure | Failure | Skip | Successful |
| 10.9.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}-n\theta}\diff{\theta} = \frac{i^{-n}}{\pi}\int_{0}^{\pi}e^{iz\cos@@{\theta}}\cos@{n\theta}\diff{\theta}} | (1)/(Pi)*int(cos(z*sin(theta)- n*theta), theta = 0..Pi)=((I)^(- n))/(Pi)*int(exp(I*z*cos(theta))*cos(n*theta), theta = 0..Pi) |
Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]- n*\[Theta]], {\[Theta], 0, Pi}]=Divide[(I)^(- n),Pi]*Integrate[Exp[I*z*Cos[\[Theta]]]*Cos[n*\[Theta]], {\[Theta], 0, Pi}] |
Failure | Failure | Skip | Successful |
| 10.9.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{0}@{z} = \frac{4}{\pi^{2}}\int_{0}^{\frac{1}{2}\pi}\cos@{z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z\sin^{2}@@{\theta}}\right)\diff{\theta}} | BesselY(0, z)=(4)/((Pi)^(2))*int(cos(z*cos(theta))*(gamma + ln(2*z*(sin(theta))^(2))), theta = 0..(1)/(2)*Pi) |
BesselY[0, z]=Divide[4,(Pi)^(2)]*Integrate[Cos[z*Cos[\[Theta]]]*(EulerGamma + Log[2*z*(Sin[\[Theta]])^(2)]), {\[Theta], 0, Divide[1,2]*Pi}] |
Failure | Failure | Skip | Successful |
| 10.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}} | BesselJ(nu, z)=(((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(cos(z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) |
BesselJ[\[Nu], z]=Divide[(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Cos[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}] |
Failure | Failure | Skip | Successful |
| 10.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{1}(1-t^{2})^{\nu-\frac{1}{2}}\cos@{zt}\diff{t}} | (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(cos(z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi)=(2*((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* cos(z*t), t = 0..1) |
Divide[(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Cos[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}]=Divide[2*(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Cos[z*t], {t, 0, 1}] |
Failure | Failure | Skip | Skip |
| 10.9.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}\left(\int_{0}^{1}(1-t^{2})^{\nu-\frac{1}{2}}\sin@{zt}\diff{t}-\int_{0}^{\infty}e^{-zt}(1+t^{2})^{\nu-\frac{1}{2}}\diff{t}\right)} | BesselY(nu, z)=(2*((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*(int((1 - (t)^(2))^(nu -(1)/(2))* sin(z*t), t = 0..1)- int(exp(- z*t)*(1 + (t)^(2))^(nu -(1)/(2)), t = 0..infinity)) |
BesselY[\[Nu], z]=Divide[2*(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*(Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Sin[z*t], {t, 0, 1}]- Integrate[Exp[- z*t]*(1 + (t)^(2))^(\[Nu]-Divide[1,2]), {t, 0, Infinity}]) |
Successful | Failure | - | Skip |
| 10.9.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-z\sinh@@{t}-\nu t}\diff{t}} | BesselJ(nu, z)=(1)/(Pi)*int(cos(z*sin(theta)- nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- z*sinh(t)- nu*t), t = 0..infinity) |
BesselJ[\[Nu], z]=Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}]-Divide[Sin[\[Nu]*Pi],Pi]*Integrate[Exp[- z*Sinh[t]- \[Nu]*t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.9.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\sin@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{1}{\pi}\int_{0}^{\infty}\left(e^{\nu t}+e^{-\nu t}\cos@{\nu\pi}\right)e^{-z\sinh@@{t}}\diff{t}} | BesselY(nu, z)=(1)/(Pi)*int(sin(z*sin(theta)- nu*theta), theta = 0..Pi)-(1)/(Pi)*int((exp(nu*t)+ exp(- nu*t)*cos(nu*Pi))* exp(- z*sinh(t)), t = 0..infinity) |
BesselY[\[Nu], z]=Divide[1,Pi]*Integrate[Sin[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}]-Divide[1,Pi]*Integrate[(Exp[\[Nu]*t]+ Exp[- \[Nu]*t]*Cos[\[Nu]*Pi])* Exp[- z*Sinh[t]], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.9#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{x} = \frac{2}{\pi}\int_{0}^{\infty}\sin@{x\cosh@@{t}-\tfrac{1}{2}\nu\pi}\cosh@{\nu t}\diff{t}} | BesselJ(nu, x)=(2)/(Pi)*int(sin(x*cosh(t)-(1)/(2)*nu*Pi)*cosh(nu*t), t = 0..infinity) |
BesselJ[\[Nu], x]=Divide[2,Pi]*Integrate[Sin[x*Cosh[t]-Divide[1,2]*\[Nu]*Pi]*Cosh[\[Nu]*t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.9#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{x} = -\frac{2}{\pi}\int_{0}^{\infty}\cos@{x\cosh@@{t}-\tfrac{1}{2}\nu\pi}\cosh@{\nu t}\diff{t}} | BesselY(nu, x)= -(2)/(Pi)*int(cos(x*cosh(t)-(1)/(2)*nu*Pi)*cosh(nu*t), t = 0..infinity) |
BesselY[\[Nu], x]= -Divide[2,Pi]*Integrate[Cos[x*Cosh[t]-Divide[1,2]*\[Nu]*Pi]*Cosh[\[Nu]*t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.9#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{0}@{x} = \frac{2}{\pi}\int_{0}^{\infty}\sin@{x\cosh@@{t}}\diff{t}} | BesselJ(0, x)=(2)/(Pi)*int(sin(x*cosh(t)), t = 0..infinity) |
BesselJ[0, x]=Divide[2,Pi]*Integrate[Sin[x*Cosh[t]], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.9#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{0}@{x} = -\frac{2}{\pi}\int_{0}^{\infty}\cos@{x\cosh@@{t}}\diff{t}} | BesselY(0, x)= -(2)/(Pi)*int(cos(x*cosh(t)), t = 0..infinity) |
BesselY[0, x]= -Divide[2,Pi]*Integrate[Cos[x*Cosh[t]], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.9.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = \frac{e^{-\frac{1}{2}\nu\pi i}}{\pi i}\int_{-\infty}^{\infty}e^{iz\cosh@@{t}-\nu t}\diff{t}} | HankelH1(nu, z)=(exp(-(1)/(2)*nu*Pi*I))/(Pi*I)*int(exp(I*z*cosh(t)- nu*t), t = - infinity..infinity) |
HankelH1[\[Nu], z]=Divide[Exp[-Divide[1,2]*\[Nu]*Pi*I],Pi*I]*Integrate[Exp[I*z*Cosh[t]- \[Nu]*t], {t, - Infinity, Infinity}] |
Failure | Failure | Skip | Error |
| 10.9.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = -\frac{e^{\frac{1}{2}\nu\pi i}}{\pi i}\int_{-\infty}^{\infty}e^{-iz\cosh@@{t}-\nu t}\diff{t}} | HankelH2(nu, z)= -(exp((1)/(2)*nu*Pi*I))/(Pi*I)*int(exp(- I*z*cosh(t)- nu*t), t = - infinity..infinity) |
HankelH2[\[Nu], z]= -Divide[Exp[Divide[1,2]*\[Nu]*Pi*I],Pi*I]*Integrate[Exp[- I*z*Cosh[t]- \[Nu]*t], {t, - Infinity, Infinity}] |
Failure | Failure | Skip | Error |
| 10.9#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{x} = \frac{2(\tfrac{1}{2}x)^{-\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\tfrac{1}{2}-\nu}}\int_{1}^{\infty}\frac{\sin@{xt}\diff{t}}{(t^{2}-1)^{\nu+\frac{1}{2}}}} | BesselJ(nu, x)=(2*((1)/(2)*x)^(- nu))/((Pi)^((1)/(2))* GAMMA((1)/(2)- nu))*int((sin(x*t))/(((t)^(2)- 1)^(nu +(1)/(2))), t = 1..infinity) |
BesselJ[\[Nu], x]=Divide[2*(Divide[1,2]*x)^(- \[Nu]),(Pi)^(Divide[1,2])* Gamma[Divide[1,2]- \[Nu]]]*Integrate[Divide[Sin[x*t],((t)^(2)- 1)^(\[Nu]+Divide[1,2])], {t, 1, Infinity}] |
Successful | Failure | - | Successful |
| 10.9#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{x} = -\frac{2(\tfrac{1}{2}x)^{-\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\tfrac{1}{2}-\nu}}\int_{1}^{\infty}\frac{\cos@{xt}\diff{t}}{(t^{2}-1)^{\nu+\frac{1}{2}}}} | BesselY(nu, x)= -(2*((1)/(2)*x)^(- nu))/((Pi)^((1)/(2))* GAMMA((1)/(2)- nu))*int((cos(x*t))/(((t)^(2)- 1)^(nu +(1)/(2))), t = 1..infinity) |
BesselY[\[Nu], x]= -Divide[2*(Divide[1,2]*x)^(- \[Nu]),(Pi)^(Divide[1,2])* Gamma[Divide[1,2]- \[Nu]]]*Integrate[Divide[Cos[x*t],((t)^(2)- 1)^(\[Nu]+Divide[1,2])], {t, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 10.9.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}\nu}\BesselJ{\nu}@{(z^{2}-\zeta^{2})^{\frac{1}{2}}} = \frac{1}{\pi}\int_{0}^{\pi}e^{\zeta\cos@@{\theta}}\cos@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-\zeta\cosh@@{t}-z\sinh@@{t}-\nu t}\diff{t}} | ((z + zeta)/(z - zeta))^((1)/(2)*nu)* BesselJ(nu, ((z)^(2)- (zeta)^(2))^((1)/(2)))=(1)/(Pi)*int(exp(zeta*cos(theta))*cos(z*sin(theta)- nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- zeta*cosh(t)- z*sinh(t)- nu*t), t = 0..infinity) |
(Divide[z + \[zeta],z - \[zeta]])^(Divide[1,2]*\[Nu])* BesselJ[\[Nu], ((z)^(2)- (\[zeta])^(2))^(Divide[1,2])]=Divide[1,Pi]*Integrate[Exp[\[zeta]*Cos[\[Theta]]]*Cos[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}]-Divide[Sin[\[Nu]*Pi],Pi]*Integrate[Exp[- \[zeta]*Cosh[t]- z*Sinh[t]- \[Nu]*t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.9.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}\nu}\BesselY{\nu}@{(z^{2}-\zeta^{2})^{\frac{1}{2}}} = \frac{1}{\pi}\int_{0}^{\pi}e^{\zeta\cos@@{\theta}}\sin@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{1}{\pi}\int_{0}^{\infty}\left(e^{\nu t+\zeta\cosh@@{t}}+e^{-\nu t-\zeta\cosh@@{t}}\cos@{\nu\pi}\right)\*e^{-z\sinh@@{t}}\diff{t}} | ((z + zeta)/(z - zeta))^((1)/(2)*nu)* BesselY(nu, ((z)^(2)- (zeta)^(2))^((1)/(2)))=(1)/(Pi)*int(exp(zeta*cos(theta))*sin(z*sin(theta)- nu*theta), theta = 0..Pi)-(1)/(Pi)*int((exp(nu*t + zeta*cosh(t))+ exp(- nu*t - zeta*cosh(t))*cos(nu*Pi))* exp(- z*sinh(t)), t = 0..infinity) |
(Divide[z + \[zeta],z - \[zeta]])^(Divide[1,2]*\[Nu])* BesselY[\[Nu], ((z)^(2)- (\[zeta])^(2))^(Divide[1,2])]=Divide[1,Pi]*Integrate[Exp[\[zeta]*Cos[\[Theta]]]*Sin[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}]-Divide[1,Pi]*Integrate[(Exp[\[Nu]*t + \[zeta]*Cosh[t]]+ Exp[- \[Nu]*t - \[zeta]*Cosh[t]]*Cos[\[Nu]*Pi])* Exp[- z*Sinh[t]], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.9.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}\nu}\HankelH{1}{\nu}@{(z^{2}-\zeta^{2})^{\frac{1}{2}}} = \frac{1}{\pi i}e^{-\frac{1}{2}\nu\pi i}\int_{-\infty}^{\infty}e^{iz\cosh@@{t}+i\zeta\sinh@@{t}-\nu t}\diff{t}} | ((z + zeta)/(z - zeta))^((1)/(2)*nu)* HankelH1(nu, ((z)^(2)- (zeta)^(2))^((1)/(2)))=(1)/(Pi*I)*exp(-(1)/(2)*nu*Pi*I)*int(exp(I*z*cosh(t)+ I*zeta*sinh(t)- nu*t), t = - infinity..infinity) |
(Divide[z + \[zeta],z - \[zeta]])^(Divide[1,2]*\[Nu])* HankelH1[\[Nu], ((z)^(2)- (\[zeta])^(2))^(Divide[1,2])]=Divide[1,Pi*I]*Exp[-Divide[1,2]*\[Nu]*Pi*I]*Integrate[Exp[I*z*Cosh[t]+ I*\[zeta]*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity}] |
Failure | Failure | Skip | Error |
| 10.9.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}\nu}\HankelH{2}{\nu}@{(z^{2}-\zeta^{2})^{\frac{1}{2}}} = -\frac{1}{\pi i}e^{\frac{1}{2}\nu\pi i}\int_{-\infty}^{\infty}e^{-iz\cosh@@{t}-i\zeta\sinh@@{t}-\nu t}\diff{t}} | ((z + zeta)/(z - zeta))^((1)/(2)*nu)* HankelH2(nu, ((z)^(2)- (zeta)^(2))^((1)/(2)))= -(1)/(Pi*I)*exp((1)/(2)*nu*Pi*I)*int(exp(- I*z*cosh(t)- I*zeta*sinh(t)- nu*t), t = - infinity..infinity) |
(Divide[z + \[zeta],z - \[zeta]])^(Divide[1,2]*\[Nu])* HankelH2[\[Nu], ((z)^(2)- (\[zeta])^(2))^(Divide[1,2])]= -Divide[1,Pi*I]*Exp[Divide[1,2]*\[Nu]*Pi*I]*Integrate[Exp[- I*z*Cosh[t]- I*\[zeta]*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity}] |
Failure | Failure | Skip | Error |
| 10.9.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty-\pi i}^{\infty+\pi i}e^{z\sinh@@{t}-\nu t}\diff{t}} | BesselJ(nu, z)=(1)/(2*Pi*I)*int(exp(z*sinh(t)- nu*t), t = infinity - Pi*I..infinity + Pi*I) |
BesselJ[\[Nu], z]=Divide[1,2*Pi*I]*Integrate[Exp[z*Sinh[t]- \[Nu]*t], {t, Infinity - Pi*I, Infinity + Pi*I}] |
Failure | Failure | Skip | Fail
Complex[0.342503927390088, -0.08973210023585859] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.3263028372306598, 4.480608248698951] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-26.41355287980499, 14.935276359740396] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.2663767645899945, 0.9702347233898156] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.9#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = \frac{1}{\pi i}\int_{-\infty}^{\infty+\pi i}e^{z\sinh@@{t}-\nu t}\diff{t}} | HankelH1(nu, z)=(1)/(Pi*I)*int(exp(z*sinh(t)- nu*t), t = - infinity..infinity + Pi*I) |
HankelH1[\[Nu], z]=Divide[1,Pi*I]*Integrate[Exp[z*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity + Pi*I}] |
Failure | Failure | Skip | Error |
| 10.9#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = -\frac{1}{\pi i}\int_{-\infty}^{\infty-\pi i}e^{z\sinh@@{t}-\nu t}\diff{t}} | HankelH2(nu, z)= -(1)/(Pi*I)*int(exp(z*sinh(t)- nu*t), t = - infinity..infinity - Pi*I) |
HankelH2[\[Nu], z]= -Divide[1,Pi*I]*Integrate[Exp[z*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity - Pi*I}] |
Failure | Failure | Skip | Error |
| 10.9.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}}{2\pi i}\int_{-\infty}^{(0+)}\exp@{t-\frac{z^{2}}{4t}}\frac{\diff{t}}{t^{\nu+1}}} | BesselJ(nu, z)=(((1)/(2)*z)^(nu))/(2*Pi*I)*int(exp(t -((z)^(2))/(4*t))*(1)/((t)^(nu + 1)), t = - infinity..(0 +)) |
BesselJ[\[Nu], z]=Divide[(Divide[1,2]*z)^(\[Nu]),2*Pi*I]*Integrate[Exp[t -Divide[(z)^(2),4*t]]*Divide[1,(t)^(\[Nu]+ 1)], {t, - Infinity, (0 +)}] |
Error | Failure | - | Error |
| 10.9.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{\EulerGamma@{\frac{1}{2}-\nu}(\frac{1}{2}z)^{\nu}}{\pi^{\frac{3}{2}}i}\int_{0}^{(1+)}\cos@{zt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}} | BesselJ(nu, z)=(GAMMA((1)/(2)- nu)*((1)/(2)*z)^(nu))/((Pi)^((3)/(2))* I)*int(cos(z*t)*((t)^(2)- 1)^(nu -(1)/(2)), t = 0..(1 +)) |
BesselJ[\[Nu], z]=Divide[Gamma[Divide[1,2]- \[Nu]]*(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[3,2])* I]*Integrate[Cos[z*t]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 0, (1 +)}] |
Error | Failure | - | Error |
| 10.9#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = \frac{\EulerGamma@{\tfrac{1}{2}-\nu}(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{3}{2}}i}\int_{1+i\infty}^{(1+)}e^{izt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}} | HankelH1(nu, z)=(GAMMA((1)/(2)- nu)*((1)/(2)*z)^(nu))/((Pi)^((3)/(2))* I)*int(exp(I*z*t)*((t)^(2)- 1)^(nu -(1)/(2)), t = 1 + I*infinity..(1 +)) |
HankelH1[\[Nu], z]=Divide[Gamma[Divide[1,2]- \[Nu]]*(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[3,2])* I]*Integrate[Exp[I*z*t]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 1 + I*Infinity, (1 +)}] |
Error | Failure | - | Error |
| 10.9#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = \frac{\EulerGamma@{\tfrac{1}{2}-\nu}(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{3}{2}}i}\int_{1-i\infty}^{(1+)}e^{-izt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}} | HankelH2(nu, z)=(GAMMA((1)/(2)- nu)*((1)/(2)*z)^(nu))/((Pi)^((3)/(2))* I)*int(exp(- I*z*t)*((t)^(2)- 1)^(nu -(1)/(2)), t = 1 - I*infinity..(1 +)) |
HankelH2[\[Nu], z]=Divide[Gamma[Divide[1,2]- \[Nu]]*(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[3,2])* I]*Integrate[Exp[- I*z*t]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 1 - I*Infinity, (1 +)}] |
Error | Failure | - | Error |
| 10.9.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{x} = \frac{1}{2\pi i}\int_{-i\infty}^{i\infty}\frac{\EulerGamma@{-t}(\tfrac{1}{2}x)^{\nu+2t}}{\EulerGamma@{\nu+t+1}}\diff{t}} | BesselJ(nu, x)=(1)/(2*Pi*I)*int((GAMMA(- t)*((1)/(2)*x)^(nu + 2*t))/(GAMMA(nu + t + 1)), t = - I*infinity..I*infinity) |
BesselJ[\[Nu], x]=Divide[1,2*Pi*I]*Integrate[Divide[Gamma[- t]*(Divide[1,2]*x)^(\[Nu]+ 2*t),Gamma[\[Nu]+ t + 1]], {t, - I*Infinity, I*Infinity}] |
Failure | Failure | Skip | Error |
| 10.9.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{1}{2\pi i}\int_{-\infty-ic}^{-\infty+ic}\frac{\EulerGamma@{t}}{\EulerGamma@{\nu-t+1}}(\tfrac{1}{2}z)^{\nu-2t}\diff{t}} | BesselJ(nu, z)=(1)/(2*Pi*I)*int((GAMMA(t))/(GAMMA(nu - t + 1))*((1)/(2)*z)^(nu - 2*t), t = - infinity - I*c..- infinity + I*c) |
BesselJ[\[Nu], z]=Divide[1,2*Pi*I]*Integrate[Divide[Gamma[t],Gamma[\[Nu]- t + 1]]*(Divide[1,2]*z)^(\[Nu]- 2*t), {t, - Infinity - I*c, - Infinity + I*c}] |
Failure | Failure | Skip | Fail
Complex[0.342503927390088, -0.08973210023585859] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.3263028372306598, 4.480608248698951] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-26.41355287980499, 14.935276359740396] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.2663767645899945, 0.9702347233898156] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.9.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = -\frac{e^{-\frac{1}{2}\nu\pi i}}{2\pi^{2}}\*\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(-\tfrac{1}{2}iz)^{\nu-2t}\diff{t}} | HankelH1(nu, z)= -(exp(-(1)/(2)*nu*Pi*I))/(2*(Pi)^(2))* int(GAMMA(t)*GAMMA(t - nu)*(-(1)/(2)*I*z)^(nu - 2*t), t = c - I*infinity..c + I*infinity) |
HankelH1[\[Nu], z]= -Divide[Exp[-Divide[1,2]*\[Nu]*Pi*I],2*(Pi)^(2)]* Integrate[Gamma[t]*Gamma[t - \[Nu]]*(-Divide[1,2]*I*z)^(\[Nu]- 2*t), {t, c - I*Infinity, c + I*Infinity}] |
Failure | Failure | Skip | Error |
| 10.9.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = \frac{e^{\frac{1}{2}\nu\pi i}}{2\pi^{2}}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(\tfrac{1}{2}iz)^{\nu-2t}\diff{t}} | HankelH2(nu, z)=(exp((1)/(2)*nu*Pi*I))/(2*(Pi)^(2))*int(GAMMA(t)*GAMMA(t - nu)*((1)/(2)*I*z)^(nu - 2*t), t = c - I*infinity..c + I*infinity) |
HankelH2[\[Nu], z]=Divide[Exp[Divide[1,2]*\[Nu]*Pi*I],2*(Pi)^(2)]*Integrate[Gamma[t]*Gamma[t - \[Nu]]*(Divide[1,2]*I*z)^(\[Nu]- 2*t), {t, c - I*Infinity, c + I*Infinity}] |
Failure | Failure | Skip | Error |
| 10.9.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\mu}@{z}\BesselJ{\nu}@{z} = \frac{2}{\pi}\int_{0}^{\pi/2}\BesselJ{\mu+\nu}@{2z\cos@@{\theta}}\cos@{(\mu-\nu)\theta}\diff{\theta}} | BesselJ(mu, z)*BesselJ(nu, z)=(2)/(Pi)*int(BesselJ(mu + nu, 2*z*cos(theta))*cos((mu - nu)* theta), theta = 0..Pi/ 2) |
BesselJ[\[Mu], z]*BesselJ[\[Nu], z]=Divide[2,Pi]*Integrate[BesselJ[\[Mu]+ \[Nu], 2*z*Cos[\[Theta]]]*Cos[(\[Mu]- \[Nu])* \[Theta]], {\[Theta], 0, Pi/ 2}] |
Failure | Failure | Skip | Skip |
| 10.9.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z}\BesselJ{\nu}@{\zeta} = \frac{2}{\pi}\int_{0}^{\pi/2}\BesselJ{2\nu}@{2(z\zeta)^{\frac{1}{2}}\sin@@{\theta}}\cos@{(z-\zeta)\cos@@{\theta}}\diff{\theta}} | BesselJ(nu, z)*BesselJ(nu, zeta)=(2)/(Pi)*int(BesselJ(2*nu, 2*(z*zeta)^((1)/(2))* sin(theta))*cos((z - zeta)* cos(theta)), theta = 0..Pi/ 2) |
BesselJ[\[Nu], z]*BesselJ[\[Nu], \[zeta]]=Divide[2,Pi]*Integrate[BesselJ[2*\[Nu], 2*(z*\[zeta])^(Divide[1,2])* Sin[\[Theta]]]*Cos[(z - \[zeta])* Cos[\[Theta]]], {\[Theta], 0, Pi/ 2}] |
Failure | Failure | Skip | Error |
| 10.9.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z}\BesselJ{\nu}@{\zeta} = \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\*\exp@{\frac{1}{2}t-\frac{z^{2}+\zeta^{2}}{2t}}\modBesselI{\nu}@{\frac{z\zeta}{t}}\frac{\diff{t}}{t}} | BesselJ(nu, z)*BesselJ(nu, zeta)=(1)/(2*Pi*I)*int(* exp((1)/(2)*t -((z)^(2)+ (zeta)^(2))/(2*t))*BesselI(nu, (z*zeta)/(t))*(1)/(t), t = c - I*infinity..c + I*infinity) |
BesselJ[\[Nu], z]*BesselJ[\[Nu], \[zeta]]=Divide[1,2*Pi*I]*Integrate[* Exp[Divide[1,2]*t -Divide[(z)^(2)+ (\[zeta])^(2),2*t]]*BesselI[\[Nu], Divide[z*\[zeta],t]]*Divide[1,t], {t, c - I*Infinity, c + I*Infinity}] |
Error | Failure | - | Error |
| 10.9.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\mu}@{x}\BesselJ{\nu}@{x} = \frac{1}{2\pi i}\int_{-i\infty}^{i\infty}\frac{\EulerGamma@{-t}\EulerGamma@{2t+\mu+\nu+1}(\tfrac{1}{2}x)^{\mu+\nu+2t}}{\EulerGamma@{t+\mu+1}\EulerGamma@{t+\nu+1}\EulerGamma@{t+\mu+\nu+1}}\diff{t}} | BesselJ(mu, x)*BesselJ(nu, x)=(1)/(2*Pi*I)*int((GAMMA(- t)*GAMMA(2*t + mu + nu + 1)*((1)/(2)*x)^(mu + nu + 2*t))/(GAMMA(t + mu + 1)*GAMMA(t + nu + 1)*GAMMA(t + mu + nu + 1)), t = - I*infinity..I*infinity) |
BesselJ[\[Mu], x]*BesselJ[\[Nu], x]=Divide[1,2*Pi*I]*Integrate[Divide[Gamma[- t]*Gamma[2*t + \[Mu]+ \[Nu]+ 1]*(Divide[1,2]*x)^(\[Mu]+ \[Nu]+ 2*t),Gamma[t + \[Mu]+ 1]*Gamma[t + \[Nu]+ 1]*Gamma[t + \[Mu]+ \[Nu]+ 1]], {t, - I*Infinity, I*Infinity}] |
Failure | Failure | Skip | Error |
| 10.9.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}^{2}@{z}+\BesselY{\nu}^{2}@{z} = \frac{8}{\pi^{2}}\int_{0}^{\infty}\cosh@{2\nu t}\modBesselK{0}@{2z\sinh@@{t}}\diff{t}} | (BesselJ(nu, z))^(2)+ (BesselY(nu, z))^(2)=(8)/((Pi)^(2))*int(cosh(2*nu*t)*BesselK(0, 2*z*sinh(t)), t = 0..infinity) |
(BesselJ[\[Nu], z])^(2)+ (BesselY[\[Nu], z])^(2)=Divide[8,(Pi)^(2)]*Integrate[Cosh[2*\[Nu]*t]*BesselK[0, 2*z*Sinh[t]], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.11.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{ze^{m\pi i}} = e^{m\nu\pi i}\BesselJ{\nu}@{z}} | BesselJ(nu, z*exp(m*Pi*I))= exp(m*nu*Pi*I)*BesselJ(nu, z) |
BesselJ[\[Nu], z*Exp[m*Pi*I]]= Exp[m*\[Nu]*Pi*I]*BesselJ[\[Nu], z] |
Failure | Failure | Fail -.3975453294+30.10329939*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}.3425382206-.8976707513e-1*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}-.3996358010+30.09969700*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}-1.326778468-4.481046040*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}... skip entries to safe data |
Fail
Complex[-0.3975452718986143, 30.10329943602099] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.34253822069590145, -0.08976707542141499] <- {Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.3996357209647074, 30.09969706489566] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-397.25907376207414, -7.293217978872368] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.11.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{ze^{m\pi i}} = e^{-m\nu\pi i}\BesselY{\nu}@{z}+2i\sin@{m\nu\pi}\cot@{\nu\pi}\BesselJ{\nu}@{z}} | BesselY(nu, z*exp(m*Pi*I))= exp(- m*nu*Pi*I)*BesselY(nu, z)+ 2*I*sin(m*nu*Pi)*cot(nu*Pi)*BesselJ(nu, z) |
BesselY[\[Nu], z*Exp[m*Pi*I]]= Exp[- m*\[Nu]*Pi*I]*BesselY[\[Nu], z]+ 2*I*Sin[m*\[Nu]*Pi]*Cot[\[Nu]*Pi]*BesselJ[\[Nu], z] |
Failure | Failure | Fail 59.96664792+53.22883098*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}-5005.486114+1251.725768*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}10758.9952-438485.5093*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}-4.21339-169.756927*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}... skip entries to safe data |
Fail
Complex[59.966647971782265, 53.22883092179323] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5005.486119861246, 1251.7257744468322] <- {Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[10758.99323773, -438485.5113105696] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[9.175550013151128, -396.6330304507175] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.11.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{\nu\pi}\HankelH{1}{\nu}@{ze^{m\pi i}} = -\sin@{(m-1)\nu\pi}\HankelH{1}{\nu}@{z}-e^{-\nu\pi i}\sin@{m\nu\pi}\HankelH{2}{\nu}@{z}} | sin(nu*Pi)*HankelH1(nu, z*exp(m*Pi*I))= - sin((m - 1)* nu*Pi)*HankelH1(nu, z)- exp(- nu*Pi*I)*sin(m*nu*Pi)*HankelH2(nu, z) |
Sin[\[Nu]*Pi]*HankelH1[\[Nu], z*Exp[m*Pi*I]]= - Sin[(m - 1)* \[Nu]*Pi]*HankelH1[\[Nu], z]- Exp[- \[Nu]*Pi*I]*Sin[m*\[Nu]*Pi]*HankelH2[\[Nu], z] |
Failure | Failure | Fail 3216.976842-3084.273397*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}-5364.683403+219295.3867*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}-17847467.19-5404443.822*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}-7000.832672-1549.801603*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}... skip entries to safe data |
Fail
Complex[3216.976837863537, -3084.273404768022] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5364.6831188620945, 219295.38712307377] <- {Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.7847467293085534*^7, -5404443.760123314] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.353713736263555, -84.22475855786759] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.11.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{\nu\pi}\HankelH{2}{\nu}@{ze^{m\pi i}} = e^{\nu\pi i}\sin@{m\nu\pi}\HankelH{1}{\nu}@{z}+\sin@{(m+1)\nu\pi}\HankelH{2}{\nu}@{z}} | sin(nu*Pi)*HankelH2(nu, z*exp(m*Pi*I))= exp(nu*Pi*I)*sin(m*nu*Pi)*HankelH1(nu, z)+ sin((m + 1)* nu*Pi)*HankelH2(nu, z) |
Sin[\[Nu]*Pi]*HankelH2[\[Nu], z*Exp[m*Pi*I]]= Exp[\[Nu]*Pi*I]*Sin[m*\[Nu]*Pi]*HankelH1[\[Nu], z]+ Sin[(m + 1)* \[Nu]*Pi]*HankelH2[\[Nu], z] |
Failure | Failure | Fail -2503.040664+625.9436263*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}5334.577216-219295.7816*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}17848181.49+5401985.686*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}7008.154936+1947.107340*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}... skip entries to safe data |
Fail
Complex[-2503.040666874715, 625.9436301275297] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5334.576217054554, -219295.782577897] <- {Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.7848181319058534*^7, 5401985.77292121] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[32720.882533131233, -8309.4971554526] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.11#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{ze^{\pi i}} = -e^{-\nu\pi i}\HankelH{2}{\nu}@{z}} | HankelH1(nu, z*exp(Pi*I))= - exp(- nu*Pi*I)*HankelH2(nu, z) |
HankelH1[\[Nu], z*Exp[Pi*I]]= - Exp[- \[Nu]*Pi*I]*HankelH2[\[Nu], z] |
Failure | Failure | Fail -53.62637626+90.06994733*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}168.4301368-8.694434719*I <- {nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-.6260433097+1.882332034*I <- {nu = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}1.189100470-.3259126629*I <- {nu = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-53.62637619369183, 90.06994740780324] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.6260433113566327, 1.8823320342787686] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.1891004703150516, 0.325912661920741] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[168.43013693288603, 8.694434886635074] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.11#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{ze^{-\pi i}} = -e^{\nu\pi i}\HankelH{1}{\nu}@{z}} | HankelH2(nu, z*exp(- Pi*I))= - exp(nu*Pi*I)*HankelH1(nu, z) |
HankelH2[\[Nu], z*Exp[- Pi*I]]= - Exp[\[Nu]*Pi*I]*HankelH1[\[Nu], z] |
Failure | Failure | Fail -.6260433097-1.882332034*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}1.189100470+.3259126629*I <- {nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-53.62637626-90.06994733*I <- {nu = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}168.4301368+8.694434719*I <- {nu = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-0.6260433113566327, -1.8823320342787686] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-53.62637619369183, -90.06994740780324] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[168.43013693288603, -8.694434886635074] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.1891004703150516, -0.325912661920741] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.11.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{n}@{ze^{m\pi i}} = (-1)^{mn}(\BesselY{n}@{z}+2im\BesselJ{n}@{z})} | BesselY(n, z*exp(m*Pi*I))=(- 1)^(m*n)*(BesselY(n, z)+ 2*I*m*BesselJ(n, z)) |
BesselY[n, z*Exp[m*Pi*I]]=(- 1)^(m*n)*(BesselY[n, z]+ 2*I*m*BesselJ[n, z]) |
Failure | Failure | - | Fail
Complex[-1.199101748008134, 3.9883106077057144] <- {Rule[m, 1], Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.9168980103888886, -0.6611177226809124] <- {Rule[m, 1], Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.5768397662292734, -0.34244579398718544] <- {Rule[m, 1], Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.199101748008134, -3.9883106077057144] <- {Rule[m, 2], Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.11.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{n}@{ze^{m\pi i}} = (-1)^{mn-1}((m-1)\HankelH{1}{n}@{z}+m\HankelH{2}{n}@{z})} | HankelH1(n, z*exp(m*Pi*I))=(- 1)^(m*n - 1)*((m - 1)*HankelH1(n, z)+ m*HankelH2(n, z)) |
HankelH1[n, z*Exp[m*Pi*I]]=(- 1)^(m*n - 1)*((m - 1)*HankelH1[n, z]+ m*HankelH2[n, z]) |
Failure | Failure | Fail -3.988310607-1.199101751*I <- {z = 2^(1/2)+I*2^(1/2), m = 1, n = 1}.6611177206+1.916898011*I <- {z = 2^(1/2)+I*2^(1/2), m = 1, n = 2}.3424457937-.5768397666*I <- {z = 2^(1/2)+I*2^(1/2), m = 1, n = 3}3.988310606+1.199101748*I <- {z = 2^(1/2)+I*2^(1/2), m = 2, n = 1}... skip entries to safe data |
Fail
Complex[-3.988310607705715, -1.1991017480081343] <- {Rule[m, 1], Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.6611177226809126, 1.9168980103888886] <- {Rule[m, 1], Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.34244579398718544, -0.5768397662292732] <- {Rule[m, 1], Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.988310607705715, 1.1991017480081343] <- {Rule[m, 2], Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.11.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{n}@{ze^{m\pi i}} = (-1)^{mn}(m\HankelH{1}{n}@{z}+(m+1)\HankelH{2}{n}@{z})} | HankelH2(n, z*exp(m*Pi*I))=(- 1)^(m*n)*(m*HankelH1(n, z)+(m + 1)*HankelH2(n, z)) |
HankelH2[n, z*Exp[m*Pi*I]]=(- 1)^(m*n)*(m*HankelH1[n, z]+(m + 1)*HankelH2[n, z]) |
Failure | Failure | Fail 3.988310606+1.199101748*I <- {z = 2^(1/2)+I*2^(1/2), m = 1, n = 1}-.6611177221-1.916898010*I <- {z = 2^(1/2)+I*2^(1/2), m = 1, n = 2}-.3424457926+.5768397669*I <- {z = 2^(1/2)+I*2^(1/2), m = 1, n = 3}-3.988310606-1.199101746*I <- {z = 2^(1/2)+I*2^(1/2), m = 2, n = 1}... skip entries to safe data |
Fail
Complex[3.988310607705715, 1.1991017480081343] <- {Rule[m, 1], Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.6611177226809126, -1.9168980103888886] <- {Rule[m, 1], Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.34244579398718566, 0.5768397662292732] <- {Rule[m, 1], Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.988310607705715, -1.1991017480081343] <- {Rule[m, 2], Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.12.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{\frac{1}{2}z(t-t^{-1})} = \sum_{m=-\infty}^{\infty}t^{m}\BesselJ{m}@{z}} | exp((1)/(2)*z*(t - (t)^(- 1)))= sum((t)^(m)* BesselJ(m, z), m = - infinity..infinity) |
Exp[Divide[1,2]*z*(t - (t)^(- 1))]= Sum[(t)^(m)* BesselJ[m, z], {m, - Infinity, Infinity}] |
Failure | Successful | Skip | - |
| 10.12#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{z\sin@@{\theta}} = \BesselJ{0}@{z}+2\sum_{k=1}^{\infty}\BesselJ{2k}@{z}\cos@{2k\theta}} | cos(z*sin(theta))= BesselJ(0, z)+ 2*sum(BesselJ(2*k, z)*cos(2*k*theta), k = 1..infinity) |
Cos[z*Sin[\[Theta]]]= BesselJ[0, z]+ 2*Sum[BesselJ[2*k, z]*Cos[2*k*\[Theta]], {k, 1, Infinity}] |
Failure | Successful | Skip | - |
| 10.12#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{z\sin@@{\theta}} = 2\sum_{k=0}^{\infty}\BesselJ{2k+1}@{z}\sin@{(2k+1)\theta}} | sin(z*sin(theta))= 2*sum(BesselJ(2*k + 1, z)*sin((2*k + 1)* theta), k = 0..infinity) |
Sin[z*Sin[\[Theta]]]= 2*Sum[BesselJ[2*k + 1, z]*Sin[(2*k + 1)* \[Theta]], {k, 0, Infinity}] |
Failure | Successful | Skip | - |
| 10.12#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{z\cos@@{\theta}} = \BesselJ{0}@{z}+2\sum_{k=1}^{\infty}(-1)^{k}\BesselJ{2k}@{z}\cos@{2k\theta}} | cos(z*cos(theta))= BesselJ(0, z)+ 2*sum((- 1)^(k)* BesselJ(2*k, z)*cos(2*k*theta), k = 1..infinity) |
Cos[z*Cos[\[Theta]]]= BesselJ[0, z]+ 2*Sum[(- 1)^(k)* BesselJ[2*k, z]*Cos[2*k*\[Theta]], {k, 1, Infinity}] |
Failure | Successful | Skip | - |
| 10.12#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{z\cos@@{\theta}} = 2\sum_{k=0}^{\infty}(-1)^{k}\BesselJ{2k+1}@{z}\cos@{(2k+1)\theta}} | sin(z*cos(theta))= 2*sum((- 1)^(k)* BesselJ(2*k + 1, z)*cos((2*k + 1)* theta), k = 0..infinity) |
Sin[z*Cos[\[Theta]]]= 2*Sum[(- 1)^(k)* BesselJ[2*k + 1, z]*Cos[(2*k + 1)* \[Theta]], {k, 0, Infinity}] |
Failure | Successful | Skip | - |
| 10.14#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{\nu}@{x}| <= 1} | abs(BesselJ(nu, x))< = 1 |
Abs[BesselJ[\[Nu], x]]< = 1 |
Failure | Failure | Fail 1.148999867 <= 1. <- {nu = 2^(1/2)+I*2^(1/2), x = 3}1.148999867 <= 1. <- {nu = 2^(1/2)-I*2^(1/2), x = 3}14.70966635 <= 1. <- {nu = -2^(1/2)-I*2^(1/2), x = 1}6.163423173 <= 1. <- {nu = -2^(1/2)-I*2^(1/2), x = 2}... skip entries to safe data |
Successful |
| 10.14#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{\nu}@{x}| <= 2^{-\frac{1}{2}}} | abs(BesselJ(nu, x))< = (2)^(-(1)/(2)) |
Abs[BesselJ[\[Nu], x]]< = (2)^(-Divide[1,2]) |
Failure | Failure | Fail .9422017731 <= .7071067810 <- {nu = 2^(1/2)+I*2^(1/2), x = 2}1.148999867 <= .7071067810 <- {nu = 2^(1/2)+I*2^(1/2), x = 3}.9422017731 <= .7071067810 <- {nu = 2^(1/2)-I*2^(1/2), x = 2}1.148999867 <= .7071067810 <- {nu = 2^(1/2)-I*2^(1/2), x = 3}... skip entries to safe data |
Successful |
| 10.14.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < \BesselJ{\nu}@{\nu}} | 0 < BesselJ(nu, nu) |
0 < BesselJ[\[Nu], \[Nu]] |
Failure | Failure | Successful | Successful |
| 10.14.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{\nu} < \frac{2^{\frac{1}{3}}}{3^{\frac{2}{3}}\EulerGamma@{\tfrac{2}{3}}\nu^{\frac{1}{3}}}} | BesselJ(nu, nu)<((2)^((1)/(3)))/((3)^((2)/(3))* GAMMA((2)/(3))*(nu)^((1)/(3))) |
BesselJ[\[Nu], \[Nu]]<Divide[(2)^(Divide[1,3]),(3)^(Divide[2,3])* Gamma[Divide[2,3]]*(\[Nu])^(Divide[1,3])] |
Failure | Failure | Successful | Successful |
| 10.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{n}@{z}| <= e^{|\imagpart@@{z}|}} | abs(BesselJ(n, z))< = exp(abs(Im(z))) |
Abs[BesselJ[n, z]]< = Exp[Abs[Im[z]]] |
Failure | Failure | Successful | Successful |
| 10.14.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{\nu}@{z}| <= \frac{|\tfrac{1}{2}z|^{\nu}e^{|\imagpart@@{z}|}}{\EulerGamma@{\nu+1}}} | abs(BesselJ(nu, z))< =((abs((1)/(2)*z))^(nu)* exp(abs(Im(z))))/(GAMMA(nu + 1)) |
Abs[BesselJ[\[Nu], z]]< =Divide[(Abs[Divide[1,2]*z])^(\[Nu])* Exp[Abs[Im[z]]],Gamma[\[Nu]+ 1]] |
Failure | Failure | Successful | Successful |
| 10.14.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{\nu}@{\nu x}| <= \frac{x^{\nu}\exp@{\nu(1-x^{2})^{\frac{1}{2}}}}{\left(1+(1-x^{2})^{\frac{1}{2}}\right)^{\nu}}} | abs(BesselJ(nu, nu*x))< =((x)^(nu)* exp(nu*(1 - (x)^(2))^((1)/(2))))/((1 +(1 - (x)^(2))^((1)/(2)))^(nu)) |
Abs[BesselJ[\[Nu], \[Nu]*x]]< =Divide[(x)^(\[Nu])* Exp[\[Nu]*(1 - (x)^(2))^(Divide[1,2])],(1 +(1 - (x)^(2))^(Divide[1,2]))^(\[Nu])] |
Failure | Failure | Skip | Successful |
| 10.14.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{\nu}'@{\nu x}| <= \frac{(1+x^{2})^{\frac{1}{4}}}{x(2\pi\nu)^{\frac{1}{2}}}\frac{x^{\nu}\exp@{\nu(1-x^{2})^{\frac{1}{2}}}}{\left(1+(1-x^{2})^{\frac{1}{2}}\right)^{\nu}}} | abs(subs( temp=nu*x, diff( BesselJ(nu, temp), temp$(1) ) ))< =((1 + (x)^(2))^((1)/(4)))/(x*(2*Pi*nu)^((1)/(2)))*((x)^(nu)* exp(nu*(1 - (x)^(2))^((1)/(2))))/((1 +(1 - (x)^(2))^((1)/(2)))^(nu)) |
Abs[D[BesselJ[\[Nu], temp], {temp, 1}]/.temp-> \[Nu]*x]< =Divide[(1 + (x)^(2))^(Divide[1,4]),x*(2*Pi*\[Nu])^(Divide[1,2])]*Divide[(x)^(\[Nu])* Exp[\[Nu]*(1 - (x)^(2))^(Divide[1,2])],(1 +(1 - (x)^(2))^(Divide[1,2]))^(\[Nu])] |
Failure | Failure | Skip | Successful |
| 10.14.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 <= \frac{\BesselJ{\nu}@{\nu x}}{x^{\nu}\BesselJ{\nu}@{\nu}}} | 1 < =(BesselJ(nu, nu*x))/((x)^(nu)* BesselJ(nu, nu)) |
1 < =Divide[BesselJ[\[Nu], \[Nu]*x],(x)^(\[Nu])* BesselJ[\[Nu], \[Nu]]] |
Failure | Failure | Skip | Successful |
| 10.14.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\BesselJ{\nu}@{\nu x}}{x^{\nu}\BesselJ{\nu}@{\nu}} <= e^{\nu(1-x)}} | (BesselJ(nu, nu*x))/((x)^(nu)* BesselJ(nu, nu))< = exp(nu*(1 - x)) |
Divide[BesselJ[\[Nu], \[Nu]*x],(x)^(\[Nu])* BesselJ[\[Nu], \[Nu]]]< = Exp[\[Nu]*(1 - x)] |
Failure | Failure | Skip | Successful |
| 10.14.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{n}@{nz}| <= \frac{\left|z^{n}\exp@{n(1-z^{2})^{\frac{1}{2}}}\right|}{\left|1+(1-z^{2})^{\frac{1}{2}}\right|^{n}}} | abs(BesselJ(n, n*z))< =(abs((z)^(n)* exp(n*(1 - (z)^(2))^((1)/(2)))))/((abs(1 +(1 - (z)^(2))^((1)/(2))))^(n)) |
Abs[BesselJ[n, n*z]]< =Divide[Abs[(z)^(n)* Exp[n*(1 - (z)^(2))^(Divide[1,2])]],(Abs[1 +(1 - (z)^(2))^(Divide[1,2])])^(n)] |
Failure | Failure | Successful | Successful |
| 10.14.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{n}@{nz}| <= 1} | abs(BesselJ(n, n*z))< = 1 |
Abs[BesselJ[n, n*z]]< = 1 |
Failure | Failure | Fail 1.041167208 <= 1. <- {z = 2^(1/2)+I*2^(1/2), n = 1}2.428697298 <= 1. <- {z = 2^(1/2)+I*2^(1/2), n = 2}6.705297847 <= 1. <- {z = 2^(1/2)+I*2^(1/2), n = 3}1.041167208 <= 1. <- {z = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Successful |
| 10.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\BesselJ{+\nu}@{z}}{\nu} = +\BesselJ{+\nu}@{z}\ln@{\tfrac{1}{2}z}-(\tfrac{1}{2}z)^{+\nu}\sum_{k=0}^{\infty}(-1)^{k}\frac{\digamma@{k+1+\nu}}{\EulerGamma@{k+1+\nu}}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!}} | diff(BesselJ(+ nu, z), nu)= + BesselJ(+ nu, z)*ln((1)/(2)*z)-((1)/(2)*z)^(+ nu)* sum((- 1)^(k)*(Psi(k + 1 + nu))/(GAMMA(k + 1 + nu))*(((1)/(4)*(z)^(2))^(k))/(factorial(k)), k = 0..infinity) |
D[BesselJ[+ \[Nu], z], \[Nu]]= + BesselJ[+ \[Nu], z]*Log[Divide[1,2]*z]-(Divide[1,2]*z)^(+ \[Nu])* Sum[(- 1)^(k)*Divide[PolyGamma[k + 1 + \[Nu]],Gamma[k + 1 + \[Nu]]]*Divide[(Divide[1,4]*(z)^(2))^(k),(k)!], {k, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 10.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\BesselJ{-\nu}@{z}}{\nu} = -\BesselJ{-\nu}@{z}\ln@{\tfrac{1}{2}z}+(\tfrac{1}{2}z)^{-\nu}\sum_{k=0}^{\infty}(-1)^{k}\frac{\digamma@{k+1-\nu}}{\EulerGamma@{k+1-\nu}}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!}} | diff(BesselJ(- nu, z), nu)= - BesselJ(- nu, z)*ln((1)/(2)*z)+((1)/(2)*z)^(- nu)* sum((- 1)^(k)*(Psi(k + 1 - nu))/(GAMMA(k + 1 - nu))*(((1)/(4)*(z)^(2))^(k))/(factorial(k)), k = 0..infinity) |
D[BesselJ[- \[Nu], z], \[Nu]]= - BesselJ[- \[Nu], z]*Log[Divide[1,2]*z]+(Divide[1,2]*z)^(- \[Nu])* Sum[(- 1)^(k)*Divide[PolyGamma[k + 1 - \[Nu]],Gamma[k + 1 - \[Nu]]]*Divide[(Divide[1,4]*(z)^(2))^(k),(k)!], {k, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 10.15.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\BesselY{\nu}@{z}}{\nu} = \cot@{\nu\pi}\left(\pderiv{\BesselJ{\nu}@{z}}{\nu}-\pi\BesselY{\nu}@{z}\right)-\csc@{\nu\pi}\pderiv{\BesselJ{-\nu}@{z}}{\nu}-\pi\BesselJ{\nu}@{z}} | diff(BesselY(nu, z), nu)= cot(nu*Pi)*(diff(BesselJ(nu, z), nu)- Pi*BesselY(nu, z))- csc(nu*Pi)*diff(BesselJ(- nu, z), nu)- Pi*BesselJ(nu, z) |
D[BesselY[\[Nu], z], \[Nu]]= Cot[\[Nu]*Pi]*(D[BesselJ[\[Nu], z], \[Nu]]- Pi*BesselY[\[Nu], z])- Csc[\[Nu]*Pi]*D[BesselJ[- \[Nu], z], \[Nu]]- Pi*BesselJ[\[Nu], z] |
Successful | Failure | - | Successful |
| 10.16#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\frac{1}{2}}@{z} = \BesselY{-\frac{1}{2}}@{z}} | BesselJ((1)/(2), z)= BesselY(-(1)/(2), z) |
BesselJ[Divide[1,2], z]= BesselY[-Divide[1,2], z] |
Successful | Successful | - | - |
| 10.16#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{-\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sin@@{z}} | BesselY(-(1)/(2), z)=((2)/(Pi*z))^((1)/(2))* sin(z) |
BesselY[-Divide[1,2], z]=(Divide[2,Pi*z])^(Divide[1,2])* Sin[z] |
Failure | Failure | Successful | Successful |
| 10.16#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{-\frac{1}{2}}@{z} = -\BesselY{\frac{1}{2}}@{z}} | BesselJ(-(1)/(2), z)= - BesselY((1)/(2), z) |
BesselJ[-Divide[1,2], z]= - BesselY[Divide[1,2], z] |
Successful | Successful | - | - |
| 10.16#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\BesselY{\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\cos@@{z}} | - BesselY((1)/(2), z)=((2)/(Pi*z))^((1)/(2))* cos(z) |
- BesselY[Divide[1,2], z]=(Divide[2,Pi*z])^(Divide[1,2])* Cos[z] |
Failure | Failure | Successful | Successful |
| 10.16#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\frac{1}{2}}@{z} = -i\HankelH{1}{-\frac{1}{2}}@{z}} | HankelH1((1)/(2), z)= - I*HankelH1(-(1)/(2), z) |
HankelH1[Divide[1,2], z]= - I*HankelH1[-Divide[1,2], z] |
Successful | Successful | - | - |
| 10.16#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -i\HankelH{1}{-\frac{1}{2}}@{z} = -i\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}e^{iz}} | - I*HankelH1(-(1)/(2), z)= - I*((2)/(Pi*z))^((1)/(2))* exp(I*z) |
- I*HankelH1[-Divide[1,2], z]= - I*(Divide[2,Pi*z])^(Divide[1,2])* Exp[I*z] |
Failure | Failure | Successful | Successful |
| 10.16#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\frac{1}{2}}@{z} = i\HankelH{2}{-\frac{1}{2}}@{z}} | HankelH2((1)/(2), z)= I*HankelH2(-(1)/(2), z) |
HankelH2[Divide[1,2], z]= I*HankelH2[-Divide[1,2], z] |
Successful | Successful | - | - |
| 10.16#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle i\HankelH{2}{-\frac{1}{2}}@{z} = i\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}e^{-iz}} | I*HankelH2(-(1)/(2), z)= I*((2)/(Pi*z))^((1)/(2))* exp(- I*z) |
I*HankelH2[-Divide[1,2], z]= I*(Divide[2,Pi*z])^(Divide[1,2])* Exp[- I*z] |
Failure | Failure | Successful | Successful |
| 10.16.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}e^{- iz}}{\EulerGamma@{\nu+1}}\KummerconfhyperM@{\nu+\tfrac{1}{2}}{2\nu+1}{+ 2iz}} | BesselJ(nu, z)=(((1)/(2)*z)^(nu)* exp(- I*z))/(GAMMA(nu + 1))*KummerM(nu +(1)/(2), 2*nu + 1, + 2*I*z) |
BesselJ[\[Nu], z]=Divide[(Divide[1,2]*z)^(\[Nu])* Exp[- I*z],Gamma[\[Nu]+ 1]]*Hypergeometric1F1[\[Nu]+Divide[1,2], 2*\[Nu]+ 1, + 2*I*z] |
Failure | Successful | Successful | - |
| 10.16.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}e^{+ iz}}{\EulerGamma@{\nu+1}}\KummerconfhyperM@{\nu+\tfrac{1}{2}}{2\nu+1}{- 2iz}} | BesselJ(nu, z)=(((1)/(2)*z)^(nu)* exp(+ I*z))/(GAMMA(nu + 1))*KummerM(nu +(1)/(2), 2*nu + 1, - 2*I*z) |
BesselJ[\[Nu], z]=Divide[(Divide[1,2]*z)^(\[Nu])* Exp[+ I*z],Gamma[\[Nu]+ 1]]*Hypergeometric1F1[\[Nu]+Divide[1,2], 2*\[Nu]+ 1, - 2*I*z] |
Failure | Successful | Successful | - |
| 10.16.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{e^{-(2\nu+1)\pi i/4}}{2^{2\nu}\EulerGamma@{\nu+1}}(2z)^{-\frac{1}{2}}\WhittakerconfhyperM{0}{\nu}@{+ 2iz}} | BesselJ(nu, z)=(exp(-(2*nu + 1)* Pi*I/ 4))/((2)^(2*nu)* GAMMA(nu + 1))*(2*z)^(-(1)/(2))* WhittakerM(0, nu, + 2*I*z) |
BesselJ[\[Nu], z]=Divide[Exp[-(2*\[Nu]+ 1)* Pi*I/ 4],(2)^(2*\[Nu])* Gamma[\[Nu]+ 1]]*(2*z)^(-Divide[1,2])* WhittakerM[0, \[Nu], + 2*I*z] |
Failure | Failure | Fail 1.497834930+.9457736110*I <- {z = -2^(1/2)+I*2^(1/2), nu = 1/4} |
Fail
Complex[1.4978349305286898, 0.945773612365157] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Rational[1, 4]]} |
| 10.16.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{e^{+(2\nu+1)\pi i/4}}{2^{2\nu}\EulerGamma@{\nu+1}}(2z)^{-\frac{1}{2}}\WhittakerconfhyperM{0}{\nu}@{- 2iz}} | BesselJ(nu, z)=(exp(+(2*nu + 1)* Pi*I/ 4))/((2)^(2*nu)* GAMMA(nu + 1))*(2*z)^(-(1)/(2))* WhittakerM(0, nu, - 2*I*z) |
BesselJ[\[Nu], z]=Divide[Exp[+(2*\[Nu]+ 1)* Pi*I/ 4],(2)^(2*\[Nu])* Gamma[\[Nu]+ 1]]*(2*z)^(-Divide[1,2])* WhittakerM[0, \[Nu], - 2*I*z] |
Failure | Failure | Fail 1.497834930-.9457736110*I <- {z = -2^(1/2)-I*2^(1/2), nu = 1/4} |
Fail
Complex[1.4978349305286898, -0.945773612365157] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ν, Rational[1, 4]]} |
| 10.16.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+1}}\genhyperF{0}{1}@{-}{\nu+1}{-\tfrac{1}{4}z^{2}}} | BesselJ(nu, z)=(((1)/(2)*z)^(nu))/(GAMMA(nu + 1))*hypergeom([-], [nu + 1], -(1)/(4)*(z)^(2)) |
BesselJ[\[Nu], z]=Divide[(Divide[1,2]*z)^(\[Nu]),Gamma[\[Nu]+ 1]]*HypergeometricPFQ[{-}, {\[Nu]+ 1}, -Divide[1,4]*(z)^(2)] |
Error | Failure | - | Error |
| 10.17.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{\frac{1}{2}} = \exp@{\tfrac{1}{2}\ln@@{|z|}+\tfrac{1}{2}i\phase@@{z}}} | (z)^((1)/(2))= exp((1)/(2)*ln(abs(z))+(1)/(2)*I*argument(z)) |
(z)^(Divide[1,2])= Exp[Divide[1,2]*Log[Abs[z]]+Divide[1,2]*I*Arg[z]] |
Failure | Failure | Successful | Successful |
| 10.17.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \scterminant{p}@{z} = \frac{e^{z}}{2\pi}\EulerGamma@{p}\incGamma@{1-p}{z}} | (exp(z)/(2*Pi))*GAMMA(p)*GAMMA(1-p,z)=(exp(z))/(2*Pi)*GAMMA(p)*GAMMA(1 - p, z) |
Error |
Successful | Error | - | - |
| 10.17.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{\ell}^{+}(\nu,z) = (-1)^{\ell}2\cos@{\nu\pi}\*\left(\sum_{k=0}^{m-1}(+ i)^{k}\frac{a_{k}(\nu)}{z^{k}}\scterminant{\ell-k}@{- 2iz}+R_{m,\ell}^{+}(\nu,z)\right)} | (R[ell])^(+)*(nu , z)=(- 1)^(ell)* 2*cos(nu*Pi)(sum((+ I)^(k)*(a[k]*(nu))/((z)^(k))*(exp(- 2*I*z)/(2*Pi))*GAMMA(ell - k)*GAMMA(1-ell - k,- 2*I*z), k = 0..m - 1)+ R(R[m , ell])^(+)*(nu , z)) |
Error |
Error | Error | - | - |
| 10.17.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{\ell}^{-}(\nu,z) = (-1)^{\ell}2\cos@{\nu\pi}\*\left(\sum_{k=0}^{m-1}(- i)^{k}\frac{a_{k}(\nu)}{z^{k}}\scterminant{\ell-k}@{+ 2iz}+R_{m,\ell}^{-}(\nu,z)\right)} | (R[ell])^(-)*(nu , z)=(- 1)^(ell)* 2*cos(nu*Pi)(sum((- I)^(k)*(a[k]*(nu))/((z)^(k))*(exp(+ 2*I*z)/(2*Pi))*GAMMA(ell - k)*GAMMA(1-ell - k,+ 2*I*z), k = 0..m - 1)+ R(R[m , ell])^(-)*(nu , z)) |
Error |
Error | Error | - | - |
| 10.19#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \assLegendreP[]{0}@{a} = 1} | LegendreP(0, a)= 1 |
LegendreP[0, 0, 3, a]= 1 |
Successful | Successful | - | - |
| 10.19#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \assLegendreP[]{1}@{a} = -\tfrac{1}{5}a} | LegendreP(1, a)= -(1)/(5)*a |
LegendreP[1, 0, 3, a]= -Divide[1,5]*a |
Failure | Failure | Fail 1.697056274+1.697056274*I <- {a = 2^(1/2)+I*2^(1/2)}1.697056274-1.697056274*I <- {a = 2^(1/2)-I*2^(1/2)}-1.697056274-1.697056274*I <- {a = -2^(1/2)-I*2^(1/2)}-1.697056274+1.697056274*I <- {a = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[1.697056274847714, 1.697056274847714] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.697056274847714, -1.697056274847714] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.697056274847714, -1.697056274847714] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.697056274847714, 1.697056274847714] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 10.19#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \assLegendreP[]{2}@{a} = -\tfrac{9}{100}a^{5}+\tfrac{3}{35}a^{2}} | LegendreP(2, a)= -(9)/(100)*(a)^(5)+(3)/(35)*(a)^(2) |
LegendreP[2, 0, 3, a]= -Divide[9,100]*(a)^(5)+Divide[3,35]*(a)^(2) |
Failure | Failure | Fail -2.536467527+3.620675327*I <- {a = 2^(1/2)+I*2^(1/2)}-2.536467527-3.620675327*I <- {a = 2^(1/2)-I*2^(1/2)}1.536467527+7.693610381*I <- {a = -2^(1/2)-I*2^(1/2)}1.536467527-7.693610381*I <- {a = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-2.5364675298172568, 3.6206753273256007] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.5364675298172568, -3.6206753273256007] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.5364675298172568, 7.693610386960114] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.5364675298172568, -7.693610386960114] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 10.19#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \assLegendreP[]{3}@{a} = \tfrac{957}{7000}a^{6}-\tfrac{173}{3150}a^{3}-\tfrac{1}{225}} | LegendreP(3, a)=(957)/(7000)*(a)^(6)-(173)/(3150)*(a)^(3)-(1)/(225) |
LegendreP[3, 0, 3, a]=Divide[957,7000]*(a)^(6)-Divide[173,3150]*(a)^(3)-Divide[1,225] |
Failure | Failure | Fail -16.56968955+21.08120757*I <- {a = 2^(1/2)+I*2^(1/2)}-16.56968955-21.08120757*I <- {a = 2^(1/2)-I*2^(1/2)}16.57857843-3.581779026*I <- {a = -2^(1/2)-I*2^(1/2)}16.57857843+3.581779026*I <- {a = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-16.569689549881762, 21.081207592921206] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-16.569689549881762, -21.081207592921206] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[16.578578438770652, -3.5817790214926353] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[16.578578438770652, 3.5817790214926353] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 10.19#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \assLegendreP[]{4}@{a} = \tfrac{27}{20000}a^{10}-\tfrac{23573}{1\;47000}a^{7}+\tfrac{5903}{1\;38600}a^{4}+\tfrac{947}{3\;46500}a} | LegendreP(4, a)=(27)/(20000)*(a)^(10)-(23573)/(147000)*(a)^(7)+(5903)/(138600)*(a)^(4)+(947)/(346500)*a |
LegendreP[4, 0, 3, a]=Divide[27,20000]*(a)^(10)-Divide[23573,147000]*(a)^(7)+Divide[5903,138600]*(a)^(4)+Divide[947,346500]*a |
Failure | Failure | Fail -54.43324245-30.90044469*I <- {a = 2^(1/2)+I*2^(1/2)}-54.43324245+30.90044469*I <- {a = 2^(1/2)-I*2^(1/2)}-83.45387141-1.864355291*I <- {a = -2^(1/2)-I*2^(1/2)}-83.45387141+1.864355291*I <- {a = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-54.4332424913453, -30.900444725067786] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-54.4332424913453, 30.900444725067786] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-83.4538715057687, -1.8643552749322136] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-83.4538715057687, 1.8643552749322136] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 10.19#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \assLegendreQ[]{0}@{a} = \tfrac{3}{10}a^{2}} | LegendreQ(0, a)=(3)/(10)*(a)^(2) |
LegendreQ[0, 0, 3, a]=Divide[3,10]*(a)^(2) |
Failure | Failure | Fail .3205774699-1.577984704*I <- {a = 2^(1/2)+I*2^(1/2)}.3205774699+1.577984704*I <- {a = 2^(1/2)-I*2^(1/2)}-.3205774699-.8220152937*I <- {a = -2^(1/2)-I*2^(1/2)}-.3205774699+.8220152937*I <- {a = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.3205774698651409, -1.5779847052119538] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.3205774698651409, 1.5779847052119538] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.3205774698651409, -0.8220152947880462] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.3205774698651409, 0.8220152947880462] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 10.19#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \assLegendreQ[]{1}@{a} = -\tfrac{17}{70}a^{3}+\tfrac{1}{70}} | LegendreQ(1, a)= -(17)/(70)*(a)^(3)+(1)/(70) |
LegendreQ[1, 0, 3, a]= -Divide[17,70]*(a)^(3)+Divide[1,70] |
Failure | Failure | Fail -1.400177072+1.292621369*I <- {a = 2^(1/2)+I*2^(1/2)}-1.400177072-1.292621369*I <- {a = 2^(1/2)-I*2^(1/2)}1.347437848-1.454993551*I <- {a = -2^(1/2)-I*2^(1/2)}1.347437848+1.454993551*I <- {a = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-1.4001770727218448, 1.2926213697851998] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4001770727218448, -1.2926213697851998] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.3474378484601681, -1.4549935513968135] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.3474378484601681, 1.4549935513968135] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 10.19#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \assLegendreQ[]{2}@{a} = -\tfrac{9}{1000}a^{7}+\tfrac{611}{3150}a^{4}-\tfrac{37}{3150}a} | LegendreQ(2, a)= -(9)/(1000)*(a)^(7)+(611)/(3150)*(a)^(4)-(37)/(3150)*a |
LegendreQ[2, 0, 3, a]= -Divide[9,1000]*(a)^(7)+Divide[611,3150]*(a)^(4)-Divide[37,3150]*a |
Failure | Failure | Fail 3.920989620-.8068387848*I <- {a = 2^(1/2)+I*2^(1/2)}3.920989620+.8068387848*I <- {a = 2^(1/2)-I*2^(1/2)}2.285994500+.8068387848*I <- {a = -2^(1/2)-I*2^(1/2)}2.285994500-.8068387848*I <- {a = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[3.920989625597779, -0.8068387862904207] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.920989625597779, 0.8068387862904207] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[2.285994501386349, 0.8068387862904207] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.285994501386349, -0.8068387862904207] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 10.19#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \assLegendreQ[]{3}@{a} = \tfrac{549}{28000}a^{8}-\tfrac{1\;10767}{6\;93000}a^{5}+\tfrac{79}{12375}a^{2}} | LegendreQ(3, a)=(549)/(28000)*(a)^(8)-(110767)/(693000)*(a)^(5)+(79)/(12375)*(a)^(2) |
LegendreQ[3, 0, 3, a]=Divide[549,28000]*(a)^(8)-Divide[110767,693000]*(a)^(5)+Divide[79,12375]*(a)^(2) |
Failure | Failure | Fail -8.639472248-3.641292303*I <- {a = 2^(1/2)+I*2^(1/2)}-8.639472248+3.641292303*I <- {a = 2^(1/2)-I*2^(1/2)}-1.406078034+3.592101911*I <- {a = -2^(1/2)-I*2^(1/2)}-1.406078034-3.592101911*I <- {a = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-8.639472261933392, -3.641292307775128] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-8.639472261933392, 3.641292307775128] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4060780379389062, 3.592101916219356] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4060780379389062, -3.592101916219356] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 10.20.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{\zeta}{z}\right)^{2} = \frac{1-z^{2}}{\zeta z^{2}}} | (diff(zeta, z))^(2)=(1 - (z)^(2))/(zeta*(z)^(2)) |
(D[\[zeta], z])^(2)=Divide[1 - (z)^(2),\[zeta]*(z)^(2)] |
Failure | Failure | Fail .4419417384-.2651650430*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}.2651650430+.4419417384*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}-.4419417384+.2651650430*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}-.2651650430-.4419417384*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Error |
| 10.20.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{3}\zeta^{\frac{3}{2}} = \int_{z}^{1}\frac{\sqrt{1-t^{2}}}{t}\diff{t}} | (2)/(3)*(zeta)^((3)/(2))= int((sqrt(1 - (t)^(2)))/(t), t = z..1) |
Divide[2,3]*(\[zeta])^(Divide[3,2])= Integrate[Divide[Sqrt[1 - (t)^(2)],t], {t, z, 1}] |
Error | Failure | - | Error |
| 10.20.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{z}^{1}\frac{\sqrt{1-t^{2}}}{t}\diff{t} = \ln@{\frac{1+\sqrt{1-z^{2}}}{z}}-\sqrt{1-z^{2}}} | int((sqrt(1 - (t)^(2)))/(t), t = z..1)= ln((1 +sqrt(1 - (z)^(2)))/(z))-sqrt(1 - (z)^(2)) |
Integrate[Divide[Sqrt[1 - (t)^(2)],t], {t, z, 1}]= Log[Divide[1 +Sqrt[1 - (z)^(2)],z]]-Sqrt[1 - (z)^(2)] |
Error | Failure | - | Error |
| 10.20.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{3}(-\zeta)^{\frac{3}{2}} = \int_{1}^{z}\frac{\sqrt{t^{2}-1}}{t}\diff{t}} | (2)/(3)*(- zeta)^((3)/(2))= int((sqrt((t)^(2)- 1))/(t), t = 1..z) |
Divide[2,3]*(- \[zeta])^(Divide[3,2])= Integrate[Divide[Sqrt[(t)^(2)- 1],t], {t, 1, z}] |
Failure | Failure | Skip | Error |
| 10.20.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{1}^{z}\frac{\sqrt{t^{2}-1}}{t}\diff{t} = \sqrt{z^{2}-1}-\asec@@{z}} | int((sqrt((t)^(2)- 1))/(t), t = 1..z)=sqrt((z)^(2)- 1)- arcsec(z) |
Integrate[Divide[Sqrt[(t)^(2)- 1],t], {t, 1, z}]=Sqrt[(z)^(2)- 1]- ArcSec[z] |
Failure | Failure | Skip | Error |
| 10.20.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = +(\tau\coth@@{\tau}-\tau^{2})^{\frac{1}{2}}+\iunit(\tau^{2}-\tau\tanh@@{\tau})^{\frac{1}{2}}} | z = +(tau*coth(tau)- (tau)^(2))^((1)/(2))+ I*((tau)^(2)- tau*tanh(tau))^((1)/(2)) |
z = +(\[Tau]*Coth[\[Tau]]- (\[Tau])^(2))^(Divide[1,2])+ I*((\[Tau])^(2)- \[Tau]*Tanh[\[Tau]])^(Divide[1,2]) |
Failure | Failure | Skip | Successful |
| 10.20.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = -(\tau\coth@@{\tau}-\tau^{2})^{\frac{1}{2}}-\iunit(\tau^{2}-\tau\tanh@@{\tau})^{\frac{1}{2}}} | z = -(tau*coth(tau)- (tau)^(2))^((1)/(2))- I*((tau)^(2)- tau*tanh(tau))^((1)/(2)) |
z = -(\[Tau]*Coth[\[Tau]]- (\[Tau])^(2))^(Divide[1,2])- I*((\[Tau])^(2)- \[Tau]*Tanh[\[Tau]])^(Divide[1,2]) |
Failure | Failure | Skip | Successful |
| 10.21.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\rho_{\nu}^{2}\deriv{\rho_{\nu}}{t}\deriv[3]{\rho_{\nu}}{t}-3\rho_{\nu}^{2}\*\left(\deriv[2]{\rho_{\nu}}{t}\right)^{2}-4\pi^{2}\rho_{\nu}^{2}\*\left(\deriv{\rho_{\nu}}{t}\right)^{2}+(4\rho_{\nu}^{2}+1-4\nu^{2})\left(\deriv{\rho_{\nu}}{t}\right)^{4} = 0} | 2*(rho[nu])^(2)*diff(rho[nu], t)*diff(rho[nu], [t$(3)])- 3*(rho[nu])^(2)*(diff(rho[nu], [t$(2)]))^(2)- 4*(Pi)^(2)* (rho[nu])^(2)*(diff(rho[nu], t))^(2)(4*rho(rho[nu])^(2)+ 1 - 4*(nu)^(2))*(diff(rho[nu], t))^(4)= 0 |
2*(Subscript[\[Rho], \[Nu]])^(2)*D[Subscript[\[Rho], \[Nu]], t]*D[Subscript[\[Rho], \[Nu]], {t, 3}]- 3*(Subscript[\[Rho], \[Nu]])^(2)*(D[Subscript[\[Rho], \[Nu]], {t, 2}])^(2)- 4*(Pi)^(2)* (Subscript[\[Rho], \[Nu]])^(2)*(D[Subscript[\[Rho], \[Nu]], t])^(2)(4*\[Rho](Subscript[\[Rho], \[Nu]])^(2)+ 1 - 4*(\[Nu])^(2))*(D[Subscript[\[Rho], \[Nu]], t])^(4)= 0 |
Successful | Successful | - | - |
| 10.21.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{c}{\nu} = 2c\int_{0}^{\infty}\modBesselK{0}@{2c\sinh@@{t}}e^{-2\nu t}\diff{t}} | diff(c, nu)= 2*c*int(BesselK(0, 2*c*sinh(t))*exp(- 2*nu*t), t = 0..infinity) |
D[c, \[Nu]]= 2*c*Integrate[BesselK[0, 2*c*Sinh[t]]*Exp[- 2*\[Nu]*t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.21.E46 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = \tfrac{1}{2}\ln@@{3}} | a =(1)/(2)*ln(3) |
a =Divide[1,2]*Log[3] |
Failure | Failure | Fail .8649074175+1.414213562*I <- {a = 2^(1/2)+I*2^(1/2)}.8649074175-1.414213562*I <- {a = 2^(1/2)-I*2^(1/2)}-1.963519706-1.414213562*I <- {a = -2^(1/2)-I*2^(1/2)}-1.963519706+1.414213562*I <- {a = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.8649074180390403, 1.4142135623730951] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8649074180390403, -1.4142135623730951] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.96351970670715, -1.4142135623730951] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.96351970670715, 1.4142135623730951] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 10.22.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{\nu}@{t}\diff{t} = 2\sum_{k=0}^{\infty}\BesselJ{\nu+2k+1}@{x}} | int(BesselJ(nu, t), t = 0..x)= 2*sum(BesselJ(nu + 2*k + 1, x), k = 0..infinity) |
Integrate[BesselJ[\[Nu], t], {t, 0, x}]= 2*Sum[BesselJ[\[Nu]+ 2*k + 1, x], {k, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 10.22.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{2n}@{t}\diff{t} = \int_{0}^{x}\BesselJ{0}@{t}\diff{t}-2\sum_{k=0}^{n-1}\BesselJ{2k+1}@{x},\quad\int_{0}^{x}\BesselJ{2n+1}@{t}\diff{t}} | int(BesselJ(2*n, t), t = 0..x)= int(BesselJ(0, t), t = 0..x)- 2*sum(BesselJ(2*k + 1, x), k = 0..n - 1), int(BesselJ(2*n + 1, t), t = 0..x) |
Integrate[BesselJ[2*n, t], {t, 0, x}]= Integrate[BesselJ[0, t], {t, 0, x}]- 2*Sum[BesselJ[2*k + 1, x], {k, 0, n - 1}], Integrate[BesselJ[2*n + 1, t], {t, 0, x}] |
Error | Failure | - | Error |
| 10.22.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{0}@{t}\diff{t}-2\sum_{k=0}^{n-1}\BesselJ{2k+1}@{x},\quad\int_{0}^{x}\BesselJ{2n+1}@{t}\diff{t} = 1-\BesselJ{0}@{x}-2\sum_{k=1}^{n}\BesselJ{2k}@{x}} | int(BesselJ(0, t), t = 0..x)- 2*sum(BesselJ(2*k + 1, x), k = 0..n - 1), int(BesselJ(2*n + 1, t), t = 0..x)= 1 - BesselJ(0, x)- 2*sum(BesselJ(2*k, x), k = 1..n) |
Integrate[BesselJ[0, t], {t, 0, x}]- 2*Sum[BesselJ[2*k + 1, x], {k, 0, n - 1}], Integrate[BesselJ[2*n + 1, t], {t, 0, x}]= 1 - BesselJ[0, x]- 2*Sum[BesselJ[2*k, x], {k, 1, n}] |
Error | Failure | - | Error |
| 10.22.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t^{\mu}\BesselJ{\nu}@{t}\diff{t} = x^{\mu}\frac{\EulerGamma@{\frac{1}{2}\nu+\frac{1}{2}\mu+\frac{1}{2}}}{\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}}}\*\sum_{k=0}^{\infty}\frac{(\nu+2k+1)\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}+k}}{\EulerGamma@{\frac{1}{2}\nu+\frac{1}{2}\mu+\frac{3}{2}+k}}\BesselJ{\nu+2k+1}@{x}} | int((t)^(mu)* BesselJ(nu, t), t = 0..x)= (x)^(mu)*(GAMMA((1)/(2)*nu +(1)/(2)*mu +(1)/(2)))/(GAMMA((1)/(2)*nu -(1)/(2)*mu +(1)/(2)))* sum(((nu + 2*k + 1)* GAMMA((1)/(2)*nu -(1)/(2)*mu +(1)/(2)+ k))/(GAMMA((1)/(2)*nu +(1)/(2)*mu +(3)/(2)+ k))*BesselJ(nu + 2*k + 1, x), k = 0..infinity) |
Integrate[(t)^(\[Mu])* BesselJ[\[Nu], t], {t, 0, x}]= (x)^(\[Mu])*Divide[Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]+Divide[1,2]],Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]+Divide[1,2]]]* Sum[Divide[(\[Nu]+ 2*k + 1)* Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]+Divide[1,2]+ k],Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]+Divide[3,2]+ k]]*BesselJ[\[Nu]+ 2*k + 1, x], {k, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 10.22.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t} = \frac{1}{2}\sum_{k=1}^{\infty}\frac{\digamma@{k+1}-\digamma@{1}}{k!}(\tfrac{1}{2}x)^{k}\BesselJ{k}@{x}} | int((1 - BesselJ(0, t))/(t), t = 0..x)=(1)/(2)*sum((Psi(k + 1)- Psi(1))/(factorial(k))*((1)/(2)*x)^(k)* BesselJ(k, x), k = 1..infinity) |
Integrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}]=Divide[1,2]*Sum[Divide[PolyGamma[k + 1]- PolyGamma[1],(k)!]*(Divide[1,2]*x)^(k)* BesselJ[k, x], {k, 1, Infinity}] |
Failure | Failure | Skip | Skip |
| 10.22.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{2\nu}@{2z\cos@@{\theta}}\cos@{2\mu\theta}\diff{\theta} = \tfrac{1}{2}\pi\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}} | int(BesselJ(2*nu, 2*z*cos(theta))*cos(2*mu*theta), theta = 0..(1)/(2)*Pi)=(1)/(2)*Pi*BesselJ(nu + mu, z)*BesselJ(nu - mu, z) |
Integrate[BesselJ[2*\[Nu], 2*z*Cos[\[Theta]]]*Cos[2*\[Mu]*\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}]=Divide[1,2]*Pi*BesselJ[\[Nu]+ \[Mu], z]*BesselJ[\[Nu]- \[Mu], z] |
Failure | Failure | Skip | Skip |
| 10.22.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi}\BesselJ{2\nu}@{2z\sin@@{\theta}}\cos@{2\mu\theta}\diff{\theta} = \pi\cos@{\mu\pi}\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}} | int(BesselJ(2*nu, 2*z*sin(theta))*cos(2*mu*theta), theta = 0..Pi)= Pi*cos(mu*Pi)*BesselJ(nu + mu, z)*BesselJ(nu - mu, z) |
Integrate[BesselJ[2*\[Nu], 2*z*Sin[\[Theta]]]*Cos[2*\[Mu]*\[Theta]], {\[Theta], 0, Pi}]= Pi*Cos[\[Mu]*Pi]*BesselJ[\[Nu]+ \[Mu], z]*BesselJ[\[Nu]- \[Mu], z] |
Failure | Failure | Skip | Skip |
| 10.22.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi}\BesselJ{2\nu}@{2z\sin@@{\theta}}\sin@{2\mu\theta}\diff{\theta} = \pi\sin@{\mu\pi}\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}} | int(BesselJ(2*nu, 2*z*sin(theta))*sin(2*mu*theta), theta = 0..Pi)= Pi*sin(mu*Pi)*BesselJ(nu + mu, z)*BesselJ(nu - mu, z) |
Integrate[BesselJ[2*\[Nu], 2*z*Sin[\[Theta]]]*Sin[2*\[Mu]*\[Theta]], {\[Theta], 0, Pi}]= Pi*Sin[\[Mu]*Pi]*BesselJ[\[Nu]+ \[Mu], z]*BesselJ[\[Nu]- \[Mu], z] |
Failure | Failure | Skip | Skip |
| 10.22.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{0}@{2z\sin@@{\theta}}\cos@{2n\theta}\diff{\theta} = \tfrac{1}{2}\pi\BesselJ{n}^{2}@{z}} | int(BesselJ(0, 2*z*sin(theta))*cos(2*n*theta), theta = 0..(1)/(2)*Pi)=(1)/(2)*Pi*(BesselJ(n, z))^(2) |
Integrate[BesselJ[0, 2*z*Sin[\[Theta]]]*Cos[2*n*\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}]=Divide[1,2]*Pi*(BesselJ[n, z])^(2) |
Failure | Failure | Skip | Successful |
| 10.22.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselY{2\nu}@{2z\cos@@{\theta}}\cos@{2\mu\theta}\diff{\theta} = \tfrac{1}{2}\pi\cot@{2\nu\pi}\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}-\tfrac{1}{2}\pi\csc@{2\nu\pi}\BesselJ{\mu-\nu}@{z}\BesselJ{-\mu-\nu}@{z}} | int(BesselY(2*nu, 2*z*cos(theta))*cos(2*mu*theta), theta = 0..(1)/(2)*Pi)=(1)/(2)*Pi*cot(2*nu*Pi)*BesselJ(nu + mu, z)*BesselJ(nu - mu, z)-(1)/(2)*Pi*csc(2*nu*Pi)*BesselJ(mu - nu, z)*BesselJ(- mu - nu, z) |
Integrate[BesselY[2*\[Nu], 2*z*Cos[\[Theta]]]*Cos[2*\[Mu]*\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}]=Divide[1,2]*Pi*Cot[2*\[Nu]*Pi]*BesselJ[\[Nu]+ \[Mu], z]*BesselJ[\[Nu]- \[Mu], z]-Divide[1,2]*Pi*Csc[2*\[Nu]*Pi]*BesselJ[\[Mu]- \[Nu], z]*BesselJ[- \[Mu]- \[Nu], z] |
Failure | Failure | Skip | Successful |
| 10.22.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselY{0}@{2z\sin@@{\theta}}\cos@{2n\theta}\diff{\theta} = \tfrac{1}{2}\pi\BesselJ{n}@{z}\BesselY{n}@{z}} | int(BesselY(0, 2*z*sin(theta))*cos(2*n*theta), theta = 0..(1)/(2)*Pi)=(1)/(2)*Pi*BesselJ(n, z)*BesselY(n, z) |
Integrate[BesselY[0, 2*z*Sin[\[Theta]]]*Cos[2*n*\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}]=Divide[1,2]*Pi*BesselJ[n, z]*BesselY[n, z] |
Failure | Failure | Skip | Successful |
| 10.22.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}(\sin@@{\theta})^{\mu+1}(\cos@@{\theta})^{2\nu+1}\diff{\theta} = 2^{\nu}\EulerGamma@{\nu+1}z^{-\nu-1}\BesselJ{\mu+\nu+1}@{z}} | int(BesselJ(mu, z*sin(theta))*(sin(theta))^(mu + 1)*(cos(theta))^(2*nu + 1), theta = 0..(1)/(2)*Pi)= (2)^(nu)* GAMMA(nu + 1)*(z)^(- nu - 1)* BesselJ(mu + nu + 1, z) |
Integrate[BesselJ[\[Mu], z*Sin[\[Theta]]]*(Sin[\[Theta]])^(\[Mu]+ 1)*(Cos[\[Theta]])^(2*\[Nu]+ 1), {\[Theta], 0, Divide[1,2]*Pi}]= (2)^(\[Nu])* Gamma[\[Nu]+ 1]*(z)^(- \[Nu]- 1)* BesselJ[\[Mu]+ \[Nu]+ 1, z] |
Successful | Failure | - | Error |
| 10.22.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}(\sin@@{\theta})^{\mu}(\cos@@{\theta})^{2\mu}\diff{\theta} = \pi^{\frac{1}{2}}2^{\mu-1}z^{-\mu}\*\EulerGamma@{\mu+\tfrac{1}{2}}\BesselJ{\mu}^{2}@{\tfrac{1}{2}z}} | int(BesselJ(mu, z*sin(theta))*(sin(theta))^(mu)*(cos(theta))^(2*mu), theta = 0..(1)/(2)*Pi)= (Pi)^((1)/(2))* (2)^(mu - 1)* (z)^(- mu)* GAMMA(mu +(1)/(2))*(BesselJ(mu, (1)/(2)*z))^(2) |
Integrate[BesselJ[\[Mu], z*Sin[\[Theta]]]*(Sin[\[Theta]])^(\[Mu])*(Cos[\[Theta]])^(2*\[Mu]), {\[Theta], 0, Divide[1,2]*Pi}]= (Pi)^(Divide[1,2])* (2)^(\[Mu]- 1)* (z)^(- \[Mu])* Gamma[\[Mu]+Divide[1,2]]*(BesselJ[\[Mu], Divide[1,2]*z])^(2) |
Successful | Failure | - | Error |
| 10.22.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselY{\mu}@{z\sin@@{\theta}}(\sin@@{\theta})^{\mu}(\cos@@{\theta})^{2\mu}\diff{\theta} = \pi^{\frac{1}{2}}2^{\mu-1}z^{-\mu}\*\EulerGamma@{\mu+\tfrac{1}{2}}\BesselJ{\mu}@{\tfrac{1}{2}z}\BesselY{\mu}@{\tfrac{1}{2}z}} | int(BesselY(mu, z*sin(theta))*(sin(theta))^(mu)*(cos(theta))^(2*mu), theta = 0..(1)/(2)*Pi)= (Pi)^((1)/(2))* (2)^(mu - 1)* (z)^(- mu)* GAMMA(mu +(1)/(2))*BesselJ(mu, (1)/(2)*z)*BesselY(mu, (1)/(2)*z) |
Integrate[BesselY[\[Mu], z*Sin[\[Theta]]]*(Sin[\[Theta]])^(\[Mu])*(Cos[\[Theta]])^(2*\[Mu]), {\[Theta], 0, Divide[1,2]*Pi}]= (Pi)^(Divide[1,2])* (2)^(\[Mu]- 1)* (z)^(- \[Mu])* Gamma[\[Mu]+Divide[1,2]]*BesselJ[\[Mu], Divide[1,2]*z]*BesselY[\[Mu], Divide[1,2]*z] |
Successful | Failure | - | Error |
| 10.22.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin^{2}@@{\theta}}\BesselJ{\nu}@{z\cos^{2}@@{\theta}}(\sin@@{\theta})^{2\mu+1}(\cos@@{\theta})^{2\nu+1}\diff{\theta} = \frac{\EulerGamma@{\mu+\tfrac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}\BesselJ{\mu+\nu+\frac{1}{2}}@{z}}{(8\pi z)^{\frac{1}{2}}\EulerGamma@{\mu+\nu+1}}} | int(BesselJ(mu, z*(sin(theta))^(2))*BesselJ(nu, z*(cos(theta))^(2))*(sin(theta))^(2*mu + 1)*(cos(theta))^(2*nu + 1), theta = 0..(1)/(2)*Pi)=(GAMMA(mu +(1)/(2))*GAMMA(nu +(1)/(2))*BesselJ(mu + nu +(1)/(2), z))/((8*Pi*z)^((1)/(2))* GAMMA(mu + nu + 1)) |
Integrate[BesselJ[\[Mu], z*(Sin[\[Theta]])^(2)]*BesselJ[\[Nu], z*(Cos[\[Theta]])^(2)]*(Sin[\[Theta]])^(2*\[Mu]+ 1)*(Cos[\[Theta]])^(2*\[Nu]+ 1), {\[Theta], 0, Divide[1,2]*Pi}]=Divide[Gamma[\[Mu]+Divide[1,2]]*Gamma[\[Nu]+Divide[1,2]]*BesselJ[\[Mu]+ \[Nu]+Divide[1,2], z],(8*Pi*z)^(Divide[1,2])* Gamma[\[Mu]+ \[Nu]+ 1]] |
Error | Failure | - | Error |
| 10.22.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin^{2}@@{\theta}}\BesselJ{\nu}@{z\cos^{2}@@{\theta}}(\sin@@{\theta})^{2\alpha-1}\sec@@{\theta}\diff{\theta} = \frac{(\mu+\nu+\alpha)\EulerGamma@{\mu+\alpha}2^{\alpha-1}}{\nu\EulerGamma@{\mu+1}z^{\alpha}}\BesselJ{\mu+\nu+\alpha}@{z}} | int(BesselJ(mu, z*(sin(theta))^(2))*BesselJ(nu, z*(cos(theta))^(2))*(sin(theta))^(2*alpha - 1)* sec(theta), theta = 0..(1)/(2)*Pi)=((mu + nu + alpha)* GAMMA(mu + alpha)*(2)^(alpha - 1))/(nu*GAMMA(mu + 1)*(z)^(alpha))*BesselJ(mu + nu + alpha, z) |
Integrate[BesselJ[\[Mu], z*(Sin[\[Theta]])^(2)]*BesselJ[\[Nu], z*(Cos[\[Theta]])^(2)]*(Sin[\[Theta]])^(2*\[Alpha]- 1)* Sec[\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}]=Divide[(\[Mu]+ \[Nu]+ \[Alpha])* Gamma[\[Mu]+ \[Alpha]]*(2)^(\[Alpha]- 1),\[Nu]*Gamma[\[Mu]+ 1]*(z)^(\[Alpha])]*BesselJ[\[Mu]+ \[Nu]+ \[Alpha], z] |
Failure | Failure | Skip | Error |
| 10.22.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin^{2}@@{\theta}}\BesselJ{\nu}@{z\cos^{2}@@{\theta}}\cot@@{\theta}\diff{\theta} = \tfrac{1}{2}\mu^{-1}\BesselJ{\mu+\nu}@{z}} | int(BesselJ(mu, z*(sin(theta))^(2))*BesselJ(nu, z*(cos(theta))^(2))*cot(theta), theta = 0..(1)/(2)*Pi)=(1)/(2)*(mu)^(- 1)* BesselJ(mu + nu, z) |
Integrate[BesselJ[\[Mu], z*(Sin[\[Theta]])^(2)]*BesselJ[\[Nu], z*(Cos[\[Theta]])^(2)]*Cot[\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}]=Divide[1,2]*(\[Mu])^(- 1)* BesselJ[\[Mu]+ \[Nu], z] |
Failure | Failure | Skip | Error |
| 10.22.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}\modBesselI{\nu}@{z\cos@@{\theta}}(\tan@@{\theta})^{\mu+1}\diff{\theta} = \frac{\EulerGamma@{\tfrac{1}{2}\nu-\tfrac{1}{2}\mu}(\tfrac{1}{2}z)^{\mu}}{2\!\EulerGamma@{\tfrac{1}{2}\nu+\tfrac{1}{2}\mu+1}}\BesselJ{\nu}@{z}} | int(BesselJ(mu, z*sin(theta))*BesselI(nu, z*cos(theta))*(tan(theta))^(mu + 1), theta = 0..(1)/(2)*Pi)=(GAMMA((1)/(2)*nu -(1)/(2)*mu)*((1)/(2)*z)^(mu))/(2*GAMMA((1)/(2)*nu +(1)/(2)*mu + 1))*BesselJ(nu, z) |
Integrate[BesselJ[\[Mu], z*Sin[\[Theta]]]*BesselI[\[Nu], z*Cos[\[Theta]]]*(Tan[\[Theta]])^(\[Mu]+ 1), {\[Theta], 0, Divide[1,2]*Pi}]=Divide[Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]]*(Divide[1,2]*z)^(\[Mu]),2*Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]+ 1]]*BesselJ[\[Nu], z] |
Failure | Failure | Skip | Error |
| 10.22.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t\BesselJ{\nu-1}^{2}@{t}\diff{t} = 2\sum_{k=0}^{\infty}(\nu+2k)\BesselJ{\nu+2k}^{2}@{x}} | int(t*(BesselJ(nu - 1, t))^(2), t = 0..x)= 2*sum((nu + 2*k)* (BesselJ(nu + 2*k, x))^(2), k = 0..infinity) |
Integrate[t*(BesselJ[\[Nu]- 1, t])^(2), {t, 0, x}]= 2*Sum[(\[Nu]+ 2*k)* (BesselJ[\[Nu]+ 2*k, x])^(2), {k, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 10.22.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t\left(\BesselJ{\nu-1}^{2}@{t}-\BesselJ{\nu+1}^{2}@{t}\right)\diff{t} = 2\nu\BesselJ{\nu}^{2}@{x}} | int(t*((BesselJ(nu - 1, t))^(2)- (BesselJ(nu + 1, t))^(2)), t = 0..x)= 2*nu*(BesselJ(nu, x))^(2) |
Integrate[t*((BesselJ[\[Nu]- 1, t])^(2)- (BesselJ[\[Nu]+ 1, t])^(2)), {t, 0, x}]= 2*\[Nu]*(BesselJ[\[Nu], x])^(2) |
Successful | Failure | - | Skip |
| 10.22.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t\BesselJ{0}^{2}@{t}\diff{t} = \tfrac{1}{2}x^{2}\left(\BesselJ{0}^{2}@{x}+\BesselJ{1}^{2}@{x}\right)} | int(t*(BesselJ(0, t))^(2), t = 0..x)=(1)/(2)*(x)^(2)*((BesselJ(0, x))^(2)+ (BesselJ(1, x))^(2)) |
Integrate[t*(BesselJ[0, t])^(2), {t, 0, x}]=Divide[1,2]*(x)^(2)*((BesselJ[0, x])^(2)+ (BesselJ[1, x])^(2)) |
Successful | Successful | - | - |
| 10.22.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{n}@{t}\BesselJ{n+1}@{t}\diff{t} = \tfrac{1}{2}\left(1-\BesselJ{0}^{2}@{x}\right)-\sum_{k=1}^{n}\BesselJ{k}^{2}@{x}} | int(BesselJ(n, t)*BesselJ(n + 1, t), t = 0..x)=(1)/(2)*(1 - (BesselJ(0, x))^(2))- sum((BesselJ(k, x))^(2), k = 1..n) |
Integrate[BesselJ[n, t]*BesselJ[n + 1, t], {t, 0, x}]=Divide[1,2]*(1 - (BesselJ[0, x])^(2))- Sum[(BesselJ[k, x])^(2), {k, 1, n}] |
Failure | Failure | Skip | Successful |
| 10.22.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\left(1-\BesselJ{0}^{2}@{x}\right)-\sum_{k=1}^{n}\BesselJ{k}^{2}@{x} = \sum_{k=n+1}^{\infty}\BesselJ{k}^{2}@{x}} | (1)/(2)*(1 - (BesselJ(0, x))^(2))- sum((BesselJ(k, x))^(2), k = 1..n)= sum((BesselJ(k, x))^(2), k = n + 1..infinity) |
Divide[1,2]*(1 - (BesselJ[0, x])^(2))- Sum[(BesselJ[k, x])^(2), {k, 1, n}]= Sum[(BesselJ[k, x])^(2), {k, n + 1, Infinity}] |
Failure | Failure | Skip | Successful |
| 10.22.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{\mu}@{t}\BesselJ{\nu}@{x-t}\diff{t} = 2\sum_{k=0}^{\infty}(-1)^{k}\BesselJ{\mu+\nu+2k+1}@{x}} | int(BesselJ(mu, t)*BesselJ(nu, x - t), t = 0..x)= 2*sum((- 1)^(k)* BesselJ(mu + nu + 2*k + 1, x), k = 0..infinity) |
Integrate[BesselJ[\[Mu], t]*BesselJ[\[Nu], x - t], {t, 0, x}]= 2*Sum[(- 1)^(k)* BesselJ[\[Mu]+ \[Nu]+ 2*k + 1, x], {k, 0, Infinity}] |
Failure | Failure | Skip | Fail
Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[μ, Rational[-1, 2]], Rule[ν, Rational[-1, 2]], Rule[Integrate[Times[BesselJ[μ, t], BesselJ[ν, Plus[Times[-1, t], x]]], {t, 0, x}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Power[-1, k], BesselJ[Plus[1, Times[2, k], μ, ν], x]], {k, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, 4.242640687119286] <- {Rule[μ, Rational[-1, 2]], Rule[ν, Rational[-1, 2]], Rule[Integrate[Times[BesselJ[μ, t], BesselJ[ν, Plus[Times[-1, t], x]]], {t, 0, x}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Power[-1, k], BesselJ[Plus[1, Times[2, k], μ, ν], x]], {k, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.242640687119286, 4.242640687119286] <- {Rule[μ, Rational[-1, 2]], Rule[ν, Rational[-1, 2]], Rule[Integrate[Times[BesselJ[μ, t], BesselJ[ν, Plus[Times[-1, t], x]]], {t, 0, x}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Power[-1, k], BesselJ[Plus[1, Times[2, k], μ, ν], x]], {k, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.242640687119286, -1.4142135623730951] <- {Rule[μ, Rational[-1, 2]], Rule[ν, Rational[-1, 2]], Rule[Integrate[Times[BesselJ[μ, t], BesselJ[ν, Plus[Times[-1, t], x]]], {t, 0, x}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Power[-1, k], BesselJ[Plus[1, Times[2, k], μ, ν], x]], {k, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.22.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{\nu}@{t}\BesselJ{1-\nu}@{x-t}\diff{t} = \BesselJ{0}@{x}-\cos@@{x}} | int(BesselJ(nu, t)*BesselJ(1 - nu, x - t), t = 0..x)= BesselJ(0, x)- cos(x) |
Integrate[BesselJ[\[Nu], t]*BesselJ[1 - \[Nu], x - t], {t, 0, x}]= BesselJ[0, x]- Cos[x] |
Failure | Failure | Skip | Successful |
| 10.22.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{\nu}@{t}\BesselJ{-\nu}@{x-t}\diff{t} = \sin@@{x}} | int(BesselJ(nu, t)*BesselJ(- nu, x - t), t = 0..x)= sin(x) |
Integrate[BesselJ[\[Nu], t]*BesselJ[- \[Nu], x - t], {t, 0, x}]= Sin[x] |
Failure | Failure | Skip | Error |
| 10.22.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t^{-1}\BesselJ{\mu}@{t}\BesselJ{\nu}@{x-t}\diff{t} = \frac{\BesselJ{\mu+\nu}@{x}}{\mu}} | int((t)^(- 1)* BesselJ(mu, t)*BesselJ(nu, x - t), t = 0..x)=(BesselJ(mu + nu, x))/(mu) |
Integrate[(t)^(- 1)* BesselJ[\[Mu], t]*BesselJ[\[Nu], x - t], {t, 0, x}]=Divide[BesselJ[\[Mu]+ \[Nu], x],\[Mu]] |
Failure | Failure | - | - |
| 10.22.E35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\frac{\BesselJ{\mu}@{t}\BesselJ{\nu}@{x-t}\diff{t}}{t(x-t)} = \frac{(\mu+\nu)\BesselJ{\mu+\nu}@{x}}{\mu\nu x}} | int((BesselJ(mu, t)*BesselJ(nu, x - t))/(t*(x - t)), t = 0..x)=((mu + nu)* BesselJ(mu + nu, x))/(mu*nu*x) |
Integrate[Divide[BesselJ[\[Mu], t]*BesselJ[\[Nu], x - t],t*(x - t)], {t, 0, x}]=Divide[(\[Mu]+ \[Nu])* BesselJ[\[Mu]+ \[Nu], x],\[Mu]*\[Nu]*x] |
Failure | Failure | Skip | Error |
| 10.22.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{\alpha}}\int_{0}^{x}(x-t)^{\alpha-1}\BesselJ{\nu}@{t}\diff{t} = 2^{\alpha}\sum_{k=0}^{\infty}\frac{(\alpha)_{k}}{k!}\BesselJ{\nu+\alpha+2k}@{x}} | (1)/(GAMMA(alpha))*int((x - t)^(alpha - 1)* BesselJ(nu, t), t = 0..x)= (2)^(alpha)* sum((alpha[k])/(factorial(k))*BesselJ(nu + alpha + 2*k, x), k = 0..infinity) |
Divide[1,Gamma[\[Alpha]]]*Integrate[(x - t)^(\[Alpha]- 1)* BesselJ[\[Nu], t], {t, 0, x}]= (2)^(\[Alpha])* Sum[Divide[Subscript[\[Alpha], k],(k)!]*BesselJ[\[Nu]+ \[Alpha]+ 2*k, x], {k, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 10.22.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}t\BesselJ{\nu}@{j_{\nu,\ell}t}\BesselJ{\nu}@{j_{\nu,m}t}\diff{t} = \tfrac{1}{2}\left(\BesselJ{\nu}'@{j_{\nu,\ell}}\right)^{2}\Kroneckerdelta{\ell}{m}} | int(t*BesselJ(nu, j[nu , ell]*t)*BesselJ(nu, j[nu , m]*t), t = 0..1)=(1)/(2)*(subs( temp=j[nu , ell], diff( BesselJ(nu, temp), temp$(1) ) ))^(2)* KroneckerDelta[ell, m] |
Integrate[t*BesselJ[\[Nu], Subscript[j, \[Nu], \[ScriptL]]*t]*BesselJ[\[Nu], Subscript[j, \[Nu], m]*t], {t, 0, 1}]=Divide[1,2]*(((D[BesselJ[\[Nu], temp], {temp, 1}]/.temp-> Subscript[j, \[Nu], \[ScriptL]])))^(2)* KroneckerDelta[\[ScriptL], m] |
Failure | Failure | Skip | Successful |
| 10.22.E38 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}t\BesselJ{\nu}@{\alpha_{\ell}t}\BesselJ{\nu}@{\alpha_{m}t}\diff{t} = \left(\frac{a^{2}}{b^{2}}+\alpha_{\ell}^{2}-\nu^{2}\right)\frac{(\BesselJ{\nu}@{\alpha_{\ell}})^{2}}{2\alpha_{\ell}^{2}}\Kroneckerdelta{\ell}{m}} | int(t*BesselJ(nu, alpha[ell]*t)*BesselJ(nu, alpha[m]*t), t = 0..1)((BesselJ(nu, alpha[ell]))^(2))/(2*alpha(alpha[ell])^(2))*KroneckerDelta[ell, m] |
Integrate[t*BesselJ[\[Nu], Subscript[\[Alpha], \[ScriptL]]*t]*BesselJ[\[Nu], Subscript[\[Alpha], m]*t], {t, 0, 1}]Divide[(BesselJ[\[Nu], Subscript[\[Alpha], \[ScriptL]]])^(2),2*\[Alpha](Subscript[\[Alpha], \[ScriptL]])^(2)]*KroneckerDelta[\[ScriptL], m] |
Failure | Failure | Skip | Successful |
| 10.22.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}\frac{\BesselJ{0}@{t}}{t}\diff{t}+\EulerConstant+\ln@{\tfrac{1}{2}x} = \int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t}} | int((BesselJ(0, t))/(t), t = x..infinity)+ gamma + ln((1)/(2)*x)= int((1 - BesselJ(0, t))/(t), t = 0..x) |
Integrate[Divide[BesselJ[0, t],t], {t, x, Infinity}]+ EulerGamma + Log[Divide[1,2]*x]= Integrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}] |
Successful | Failure | - | Successful |
| 10.22.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t} = \sum_{k=1}^{\infty}(-1)^{k-1}\frac{(\frac{1}{2}x)^{2k}}{2k(k!)^{2}}} | int((1 - BesselJ(0, t))/(t), t = 0..x)= sum((- 1)^(k - 1)*(((1)/(2)*x)^(2*k))/(2*k*(factorial(k))^(2)), k = 1..infinity) |
Integrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}]= Sum[(- 1)^(k - 1)*Divide[(Divide[1,2]*x)^(2*k),2*k*((k)!)^(2)], {k, 1, Infinity}] |
Successful | Failure | - | Successful |
| 10.22.E40 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}\frac{\BesselY{0}@{t}}{t}\diff{t} = -\frac{1}{\pi}\left(\ln@{\tfrac{1}{2}x}+\EulerConstant\right)^{2}+\frac{\pi}{6}+\frac{2}{\pi}\sum_{k=1}^{\infty}(-1)^{k}\*\left(\digamma@{k+1}+\frac{1}{2k}-\ln@{\tfrac{1}{2}x}\right)\frac{(\tfrac{1}{2}x)^{2k}}{2k(k!)^{2}}} | int((BesselY(0, t))/(t), t = x..infinity)= -(1)/(Pi)*(ln((1)/(2)*x)+ gamma)^(2)+(Pi)/(6)+(2)/(Pi)*sum((- 1)^(k)*(Psi(k + 1)+(1)/(2*k)- ln((1)/(2)*x))*(((1)/(2)*x)^(2*k))/(2*k*(factorial(k))^(2)), k = 1..infinity) |
Integrate[Divide[BesselY[0, t],t], {t, x, Infinity}]= -Divide[1,Pi]*(Log[Divide[1,2]*x]+ EulerGamma)^(2)+Divide[Pi,6]+Divide[2,Pi]*Sum[(- 1)^(k)*(PolyGamma[k + 1]+Divide[1,2*k]- Log[Divide[1,2]*x])*Divide[(Divide[1,2]*x)^(2*k),2*k*((k)!)^(2)], {k, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 10.22.E41 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\nu}@{t}\diff{t} = 1} | int(BesselJ(nu, t), t = 0..infinity)= 1 |
Integrate[BesselJ[\[Nu], t], {t, 0, Infinity}]= 1 |
Successful | Failure | - | Successful |
| 10.22.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselY{\nu}@{t}\diff{t} = -\tan@{\tfrac{1}{2}\nu\pi}} | int(BesselY(nu, t), t = 0..infinity)= - tan((1)/(2)*nu*Pi) |
Integrate[BesselY[\[Nu], t], {t, 0, Infinity}]= - Tan[Divide[1,2]*\[Nu]*Pi] |
Successful | Failure | - | Error |
| 10.22.E43 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu}\BesselJ{\nu}@{t}\diff{t} = 2^{\mu}\frac{\EulerGamma@{\tfrac{1}{2}\nu+\tfrac{1}{2}\mu+\tfrac{1}{2}}}{\EulerGamma@{\tfrac{1}{2}\nu-\tfrac{1}{2}\mu+\tfrac{1}{2}}}} | int((t)^(mu)* BesselJ(nu, t), t = 0..infinity)= (2)^(mu)*(GAMMA((1)/(2)*nu +(1)/(2)*mu +(1)/(2)))/(GAMMA((1)/(2)*nu -(1)/(2)*mu +(1)/(2))) |
Integrate[(t)^(\[Mu])* BesselJ[\[Nu], t], {t, 0, Infinity}]= (2)^(\[Mu])*Divide[Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]+Divide[1,2]],Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]+Divide[1,2]]] |
Successful | Failure | - | Successful |
| 10.22.E44 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu}\BesselY{\nu}@{t}\diff{t} = \frac{2^{\mu}}{\pi}\EulerGamma@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}}\EulerGamma@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2}}\sin@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu}\pi} | int((t)^(mu)* BesselY(nu, t), t = 0..infinity)=((2)^(mu))/(Pi)*GAMMA((1)/(2)*mu +(1)/(2)*nu +(1)/(2))*GAMMA((1)/(2)*mu -(1)/(2)*nu +(1)/(2))*sin((1)/(2)*mu -(1)/(2)*nu)*Pi |
Integrate[(t)^(\[Mu])* BesselY[\[Nu], t], {t, 0, Infinity}]=Divide[(2)^(\[Mu]),Pi]*Gamma[Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]+Divide[1,2]]*Gamma[Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]+Divide[1,2]]*Sin[Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]]*Pi |
Failure | Failure | Skip | Error |
| 10.22.E45 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{1-\BesselJ{0}@{t}}{t^{\mu}}\diff{t} = -\frac{\pi\sec@{\frac{1}{2}\mu\pi}}{2^{\mu}\EulerGamma^{2}@{\frac{1}{2}\mu+\frac{1}{2}}}} | int((1 - BesselJ(0, t))/((t)^(mu)), t = 0..infinity)= -(Pi*sec((1)/(2)*mu*Pi))/((2)^(mu)* (GAMMA((1)/(2)*mu +(1)/(2)))^(2)) |
Integrate[Divide[1 - BesselJ[0, t],(t)^(\[Mu])], {t, 0, Infinity}]= -Divide[Pi*Sec[Divide[1,2]*\[Mu]*Pi],(2)^(\[Mu])* (Gamma[Divide[1,2]*\[Mu]+Divide[1,2]])^(2)] |
Failure | Failure | Skip | Error |
| 10.22.E46 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{t^{\nu+1}\BesselJ{\nu}@{at}}{(t^{2}+b^{2})^{\mu+1}}\diff{t} = \frac{a^{\mu}b^{\nu-\mu}}{2^{\mu}\EulerGamma@{\mu+1}}\modBesselK{\nu-\mu}@{ab}} | int(((t)^(nu + 1)* BesselJ(nu, a*t))/(((t)^(2)+ (b)^(2))^(mu + 1)), t = 0..infinity)=((a)^(mu)* (b)^(nu - mu))/((2)^(mu)* GAMMA(mu + 1))*BesselK(nu - mu, a*b) |
Integrate[Divide[(t)^(\[Nu]+ 1)* BesselJ[\[Nu], a*t],((t)^(2)+ (b)^(2))^(\[Mu]+ 1)], {t, 0, Infinity}]=Divide[(a)^(\[Mu])* (b)^(\[Nu]- \[Mu]),(2)^(\[Mu])* Gamma[\[Mu]+ 1]]*BesselK[\[Nu]- \[Mu], a*b] |
Failure | Failure | Skip | Error |
| 10.22.E47 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{t^{\nu}\BesselY{\nu}@{at}}{t^{2}+b^{2}}\diff{t} = -b^{\nu-1}\modBesselK{\nu}@{ab}} | int(((t)^(nu)* BesselY(nu, a*t))/((t)^(2)+ (b)^(2)), t = 0..infinity)= - (b)^(nu - 1)* BesselK(nu, a*b) |
Integrate[Divide[(t)^(\[Nu])* BesselY[\[Nu], a*t],(t)^(2)+ (b)^(2)], {t, 0, Infinity}]= - (b)^(\[Nu]- 1)* BesselK[\[Nu], a*b] |
Failure | Failure | Skip | Error |
| 10.22.E48 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\mu}@{x\cosh@@{\phi}}(\cosh@@{\phi})^{1-\mu}(\sinh@@{\phi})^{2\nu+1}\diff{\phi} = 2^{\nu}\EulerGamma@{\nu+1}x^{-\nu-1}\BesselJ{\mu-\nu-1}@{x}} | int(BesselJ(mu, x*cosh(phi))*(cosh(phi))^(1 - mu)*(sinh(phi))^(2*nu + 1), phi = 0..infinity)= (2)^(nu)* GAMMA(nu + 1)*(x)^(- nu - 1)* BesselJ(mu - nu - 1, x) |
Integrate[BesselJ[\[Mu], x*Cosh[\[Phi]]]*(Cosh[\[Phi]])^(1 - \[Mu])*(Sinh[\[Phi]])^(2*\[Nu]+ 1), {\[Phi], 0, Infinity}]= (2)^(\[Nu])* Gamma[\[Nu]+ 1]*(x)^(- \[Nu]- 1)* BesselJ[\[Mu]- \[Nu]- 1, x] |
Failure | Failure | Skip | Error |
| 10.22.E49 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu-1}e^{-at}\BesselJ{\nu}@{bt}\diff{t} = \frac{(\tfrac{1}{2}b)^{\nu}}{a^{\mu+\nu}}\EulerGamma@{\mu+\nu}\*\hyperOlverF@{\frac{\mu+\nu}{2}}{\frac{\mu+\nu+1}{2}}{\nu+1}{-\frac{b^{2}}{a^{2}}}} | int((t)^(mu - 1)* exp(- a*t)*BesselJ(nu, b*t), t = 0..infinity)=(((1)/(2)*b)^(nu))/((a)^(mu + nu))*GAMMA(mu + nu)* hypergeom([(mu + nu)/(2), (mu + nu + 1)/(2)], [nu + 1], -((b)^(2))/((a)^(2)))/GAMMA(nu + 1) |
Integrate[(t)^(\[Mu]- 1)* Exp[- a*t]*BesselJ[\[Nu], b*t], {t, 0, Infinity}]=Divide[(Divide[1,2]*b)^(\[Nu]),(a)^(\[Mu]+ \[Nu])]*Gamma[\[Mu]+ \[Nu]]* Hypergeometric2F1Regularized[Divide[\[Mu]+ \[Nu],2], Divide[\[Mu]+ \[Nu]+ 1,2], \[Nu]+ 1, -Divide[(b)^(2),(a)^(2)]] |
Failure | Failure | Skip | Error |
| 10.22.E50 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu-1}e^{-at}\BesselY{\nu}@{bt}\diff{t} = \cot@{\nu\pi}\frac{(\tfrac{1}{2}b)^{\nu}\EulerGamma@{\mu+\nu}}{(a^{2}+b^{2})^{\frac{1}{2}(\mu+\nu)}}\*\hyperOlverF@{\frac{\mu+\nu}{2}}{\frac{1-\mu+\nu}{2}}{\nu+1}{\frac{b^{2}}{a^{2}+b^{2}}}-\csc@{\nu\pi}\frac{(\tfrac{1}{2}b)^{-\nu}\EulerGamma@{\mu-\nu}}{(a^{2}+b^{2})^{\frac{1}{2}(\mu-\nu)}}\*\hyperOlverF@{\frac{\mu-\nu}{2}}{\frac{1-\mu-\nu}{2}}{1-\nu}{\frac{b^{2}}{a^{2}+b^{2}}}} | int((t)^(mu - 1)* exp(- a*t)*BesselY(nu, b*t), t = 0..infinity)= cot(nu*Pi)*(((1)/(2)*b)^(nu)* GAMMA(mu + nu))/(((a)^(2)+ (b)^(2))^((1)/(2)*(mu + nu)))* hypergeom([(mu + nu)/(2), (1 - mu + nu)/(2)], [nu + 1], ((b)^(2))/((a)^(2)+ (b)^(2)))/GAMMA(nu + 1)- csc(nu*Pi)*(((1)/(2)*b)^(- nu)* GAMMA(mu - nu))/(((a)^(2)+ (b)^(2))^((1)/(2)*(mu - nu)))* hypergeom([(mu - nu)/(2), (1 - mu - nu)/(2)], [1 - nu], ((b)^(2))/((a)^(2)+ (b)^(2)))/GAMMA(1 - nu) |
Integrate[(t)^(\[Mu]- 1)* Exp[- a*t]*BesselY[\[Nu], b*t], {t, 0, Infinity}]= Cot[\[Nu]*Pi]*Divide[(Divide[1,2]*b)^(\[Nu])* Gamma[\[Mu]+ \[Nu]],((a)^(2)+ (b)^(2))^(Divide[1,2]*(\[Mu]+ \[Nu]))]* Hypergeometric2F1Regularized[Divide[\[Mu]+ \[Nu],2], Divide[1 - \[Mu]+ \[Nu],2], \[Nu]+ 1, Divide[(b)^(2),(a)^(2)+ (b)^(2)]]- Csc[\[Nu]*Pi]*Divide[(Divide[1,2]*b)^(- \[Nu])* Gamma[\[Mu]- \[Nu]],((a)^(2)+ (b)^(2))^(Divide[1,2]*(\[Mu]- \[Nu]))]* Hypergeometric2F1Regularized[Divide[\[Mu]- \[Nu],2], Divide[1 - \[Mu]- \[Nu],2], 1 - \[Nu], Divide[(b)^(2),(a)^(2)+ (b)^(2)]] |
Failure | Failure | Skip | Error |
| 10.22.E51 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\nu}@{bt}\exp@{-p^{2}t^{2}}t^{\nu+1}\diff{t} = \frac{b^{\nu}}{(2p^{2})^{\nu+1}}\exp@{-\frac{b^{2}}{4p^{2}}}} | int(BesselJ(nu, b*t)*exp(- (p)^(2)* (t)^(2))*(t)^(nu + 1), t = 0..infinity)=((b)^(nu))/((2*(p)^(2))^(nu + 1))*exp(-((b)^(2))/(4*(p)^(2))) |
Integrate[BesselJ[\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)]*(t)^(\[Nu]+ 1), {t, 0, Infinity}]=Divide[(b)^(\[Nu]),(2*(p)^(2))^(\[Nu]+ 1)]*Exp[-Divide[(b)^(2),4*(p)^(2)]] |
Successful | Failure | - | Error |
| 10.22.E52 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{\sqrt{\pi}}{2p}\exp@{-\frac{b^{2}}{8p^{2}}}\modBesselI{\ifrac{\nu}{2}}@{\frac{b^{2}}{8p^{2}}}} | int(BesselJ(nu, b*t)*exp(- (p)^(2)* (t)^(2)), t = 0..infinity)=(sqrt(Pi))/(2*p)*exp(-((b)^(2))/(8*(p)^(2)))*BesselI((nu)/(2), ((b)^(2))/(8*(p)^(2))) |
Integrate[BesselJ[\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}]=Divide[Sqrt[Pi],2*p]*Exp[-Divide[(b)^(2),8*(p)^(2)]]*BesselI[Divide[\[Nu],2], Divide[(b)^(2),8*(p)^(2)]] |
Failure | Failure | Skip | Error |
| 10.22.E53 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselY{2\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = -\frac{\sqrt{\pi}}{2p}\exp@{-\frac{b^{2}}{8p^{2}}}\left(\modBesselI{\nu}@{\frac{b^{2}}{8p^{2}}}\tan@{\nu\pi}+\frac{1}{\pi}\modBesselK{\nu}@{\frac{b^{2}}{8p^{2}}}\sec@{\nu\pi}\right)} | int(BesselY(2*nu, b*t)*exp(- (p)^(2)* (t)^(2)), t = 0..infinity)= -(sqrt(Pi))/(2*p)*exp(-((b)^(2))/(8*(p)^(2)))*(BesselI(nu, ((b)^(2))/(8*(p)^(2)))*tan(nu*Pi)+(1)/(Pi)*BesselK(nu, ((b)^(2))/(8*(p)^(2)))*sec(nu*Pi)) |
Integrate[BesselY[2*\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}]= -Divide[Sqrt[Pi],2*p]*Exp[-Divide[(b)^(2),8*(p)^(2)]]*(BesselI[\[Nu], Divide[(b)^(2),8*(p)^(2)]]*Tan[\[Nu]*Pi]+Divide[1,Pi]*BesselK[\[Nu], Divide[(b)^(2),8*(p)^(2)]]*Sec[\[Nu]*Pi]) |
Failure | Failure | Skip | Error |
| 10.22.E54 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\nu}@{bt}\exp@{-p^{2}t^{2}}t^{\mu-1}\diff{t} = \frac{(\tfrac{1}{2}b/p)^{\nu}\EulerGamma@{\tfrac{1}{2}\nu+\tfrac{1}{2}\mu}}{2p^{\mu}}\exp@{-\frac{b^{2}}{4p^{2}}}\*\OlverconfhyperM@{\tfrac{1}{2}\nu-\tfrac{1}{2}\mu+1}{\nu+1}{\frac{b^{2}}{4p^{2}}}} | int(BesselJ(nu, b*t)*exp(- (p)^(2)* (t)^(2))*(t)^(mu - 1), t = 0..infinity)=(((1)/(2)*b/ p)^(nu)* GAMMA((1)/(2)*nu +(1)/(2)*mu))/(2*(p)^(mu))*exp(-((b)^(2))/(4*(p)^(2)))* KummerM((1)/(2)*nu -(1)/(2)*mu + 1, nu + 1, ((b)^(2))/(4*(p)^(2)))/GAMMA(nu + 1) |
Integrate[BesselJ[\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)]*(t)^(\[Mu]- 1), {t, 0, Infinity}]=Divide[(Divide[1,2]*b/ p)^(\[Nu])* Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]],2*(p)^(\[Mu])]*Exp[-Divide[(b)^(2),4*(p)^(2)]]* Hypergeometric1F1Regularized[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]+ 1, \[Nu]+ 1, Divide[(b)^(2),4*(p)^(2)]] |
Failure | Failure | Skip | Error |
| 10.22.E55 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{-1}\BesselJ{\nu+2\ell+1}@{t}\BesselJ{\nu+2m+1}@{t}\diff{t} = \frac{\Kroneckerdelta{\ell}{m}}{2(2\ell+\nu+1)}} | int((t)^(- 1)* BesselJ(nu + 2*ell + 1, t)*BesselJ(nu + 2*m + 1, t), t = 0..infinity)=(KroneckerDelta[ell, m])/(2*(2*ell + nu + 1)) |
Integrate[(t)^(- 1)* BesselJ[\[Nu]+ 2*\[ScriptL]+ 1, t]*BesselJ[\[Nu]+ 2*m + 1, t], {t, 0, Infinity}]=Divide[KroneckerDelta[\[ScriptL], m],2*(2*\[ScriptL]+ \[Nu]+ 1)] |
Failure | Failure | Skip | Successful |
| 10.22.E56 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{\BesselJ{\mu}@{at}\BesselJ{\nu}@{bt}}{t^{\lambda}}\diff{t} = \frac{a^{\mu}\EulerGamma@{\frac{1}{2}\nu+\frac{1}{2}\mu-\frac{1}{2}\lambda+\frac{1}{2}}}{2^{\lambda}b^{\mu-\lambda+1}\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}\lambda+\frac{1}{2}}}\*\hyperOlverF@{\tfrac{1}{2}(\mu+\nu-\lambda+1)}{\tfrac{1}{2}(\mu-\nu-\lambda+1)}{\mu+1}{\frac{a^{2}}{b^{2}}}} | int((BesselJ(mu, a*t)*BesselJ(nu, b*t))/((t)^(lambda)), t = 0..infinity)=((a)^(mu)* GAMMA((1)/(2)*nu +(1)/(2)*mu -(1)/(2)*lambda +(1)/(2)))/((2)^(lambda)* (b)^(mu - lambda + 1)* GAMMA((1)/(2)*nu -(1)/(2)*mu +(1)/(2)*lambda +(1)/(2)))* hypergeom([(1)/(2)*(mu + nu - lambda + 1), (1)/(2)*(mu - nu - lambda + 1)], [mu + 1], ((a)^(2))/((b)^(2)))/GAMMA(mu + 1) |
Integrate[Divide[BesselJ[\[Mu], a*t]*BesselJ[\[Nu], b*t],(t)^(\[Lambda])], {t, 0, Infinity}]=Divide[(a)^(\[Mu])* Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]-Divide[1,2]*\[Lambda]+Divide[1,2]],(2)^(\[Lambda])* (b)^(\[Mu]- \[Lambda]+ 1)* Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]+Divide[1,2]*\[Lambda]+Divide[1,2]]]* Hypergeometric2F1Regularized[Divide[1,2]*(\[Mu]+ \[Nu]- \[Lambda]+ 1), Divide[1,2]*(\[Mu]- \[Nu]- \[Lambda]+ 1), \[Mu]+ 1, Divide[(a)^(2),(b)^(2)]] |
Failure | Failure | Skip | Error |
| 10.22.E57 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{\BesselJ{\mu}@{at}\BesselJ{\nu}@{at}}{t^{\lambda}}\diff{t} = \frac{(\frac{1}{2}a)^{\lambda-1}\EulerGamma@{\frac{1}{2}\mu+\frac{1}{2}\nu-\frac{1}{2}\lambda+\frac{1}{2}}\EulerGamma@{\lambda}}{2\EulerGamma@{\frac{1}{2}\lambda+\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}}\EulerGamma@{\frac{1}{2}\lambda+\frac{1}{2}\mu-\frac{1}{2}\nu+\frac{1}{2}}\EulerGamma@{\frac{1}{2}\lambda+\frac{1}{2}\mu+\frac{1}{2}\nu+\frac{1}{2}}}} | int((BesselJ(mu, a*t)*BesselJ(nu, a*t))/((t)^(lambda)), t = 0..infinity)=(((1)/(2)*a)^(lambda - 1)* GAMMA((1)/(2)*mu +(1)/(2)*nu -(1)/(2)*lambda +(1)/(2))*GAMMA(lambda))/(2*GAMMA((1)/(2)*lambda +(1)/(2)*nu -(1)/(2)*mu +(1)/(2))*GAMMA((1)/(2)*lambda +(1)/(2)*mu -(1)/(2)*nu +(1)/(2))*GAMMA((1)/(2)*lambda +(1)/(2)*mu +(1)/(2)*nu +(1)/(2))) |
Integrate[Divide[BesselJ[\[Mu], a*t]*BesselJ[\[Nu], a*t],(t)^(\[Lambda])], {t, 0, Infinity}]=Divide[(Divide[1,2]*a)^(\[Lambda]- 1)* Gamma[Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]-Divide[1,2]*\[Lambda]+Divide[1,2]]*Gamma[\[Lambda]],2*Gamma[Divide[1,2]*\[Lambda]+Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]+Divide[1,2]]*Gamma[Divide[1,2]*\[Lambda]+Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]+Divide[1,2]]*Gamma[Divide[1,2]*\[Lambda]+Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]+Divide[1,2]]] |
Failure | Failure | Skip | Error |
| 10.22.E58 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{\BesselJ{\nu}@{at}\BesselJ{\nu}@{bt}}{t^{\lambda}}\diff{t} = \frac{(ab)^{\nu}\EulerGamma@{\nu-\frac{1}{2}\lambda+\frac{1}{2}}}{2^{\lambda}(a^{2}+b^{2})^{\nu-\frac{1}{2}\lambda+\frac{1}{2}}\EulerGamma@{\frac{1}{2}\lambda+\frac{1}{2}}}\hyperOlverF@{\frac{2\nu+1-\lambda}{4}}{\frac{2\nu+3-\lambda}{4}}{\nu+1}{\frac{4a^{2}b^{2}}{(a^{2}+b^{2})^{2}}}} | int((BesselJ(nu, a*t)*BesselJ(nu, b*t))/((t)^(lambda)), t = 0..infinity)=((a*b)^(nu)* GAMMA(nu -(1)/(2)*lambda +(1)/(2)))/((2)^(lambda)*((a)^(2)+ (b)^(2))^(nu -(1)/(2)*lambda +(1)/(2))* GAMMA((1)/(2)*lambda +(1)/(2)))*hypergeom([(2*nu + 1 - lambda)/(4), (2*nu + 3 - lambda)/(4)], [nu + 1], (4*(a)^(2)* (b)^(2))/(((a)^(2)+ (b)^(2))^(2)))/GAMMA(nu + 1) |
Integrate[Divide[BesselJ[\[Nu], a*t]*BesselJ[\[Nu], b*t],(t)^(\[Lambda])], {t, 0, Infinity}]=Divide[(a*b)^(\[Nu])* Gamma[\[Nu]-Divide[1,2]*\[Lambda]+Divide[1,2]],(2)^(\[Lambda])*((a)^(2)+ (b)^(2))^(\[Nu]-Divide[1,2]*\[Lambda]+Divide[1,2])* Gamma[Divide[1,2]*\[Lambda]+Divide[1,2]]]*Hypergeometric2F1Regularized[Divide[2*\[Nu]+ 1 - \[Lambda],4], Divide[2*\[Nu]+ 3 - \[Lambda],4], \[Nu]+ 1, Divide[4*(a)^(2)* (b)^(2),((a)^(2)+ (b)^(2))^(2)]] |
Failure | Failure | Skip | Error |
| 10.22.E59 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{ibt}\BesselJ{\mu}@{at}\diff{t} = \begin{cases}\dfrac{\exp@{i\mu\asin@{b/a}}}{(a^{2}-b^{2})^{\frac{1}{2}}},&0} | int(exp(I*b*t)*BesselJ(mu, a*t), t = 0..infinity)= |
Integrate[Exp[I*b*t]*BesselJ[\[Mu], a*t], {t, 0, Infinity}]= |
Error | Failure | - | - |
| 10.22.E59 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{cases}\dfrac{\exp@{i\mu\asin@{b/a}}}{(a^{2}-b^{2})^{\frac{1}{2}}},&0 <= b} | |
|
Error | Failure | - | Error |
| 10.22.E60 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{ibt}\BesselY{0}@{at}\diff{t} = \begin{cases}(2i/\pi)(a^{2}-b^{2})^{-\frac{1}{2}}\asin@{b/a},&0} | int(exp(I*b*t)*BesselY(0, a*t), t = 0..infinity)= |
Integrate[Exp[I*b*t]*BesselY[0, a*t], {t, 0, Infinity}]= |
Error | Failure | - | - |
| 10.22.E60 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{cases}(2i/\pi)(a^{2}-b^{2})^{-\frac{1}{2}}\asin@{b/a},&0 <= b} | |
|
Error | Failure | - | Error |
| 10.22.E61 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{-1}e^{ibt}\BesselJ{\mu}@{at}\diff{t} = \begin{cases}(1/\mu)\exp@{i\mu\asin@{b/a}},&0} | int((t)^(- 1)* exp(I*b*t)*BesselJ(mu, a*t), t = 0..infinity)= |
Integrate[(t)^(- 1)* Exp[I*b*t]*BesselJ[\[Mu], a*t], {t, 0, Infinity}]= |
Error | Failure | - | - |
| 10.22.E61 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{cases}(1/\mu)\exp@{i\mu\asin@{b/a}},&0 <= b} | |
|
Error | Failure | - | Error |
| 10.22.E62 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu-\nu+1}\BesselJ{\mu}@{at}\BesselJ{\nu}@{bt}\diff{t} = \begin{cases}0,&0} | int((t)^(mu - nu + 1)* BesselJ(mu, a*t)*BesselJ(nu, b*t), t = 0..infinity)= |
Integrate[(t)^(\[Mu]- \[Nu]+ 1)* BesselJ[\[Mu], a*t]*BesselJ[\[Nu], b*t], {t, 0, Infinity}]= |
Error | Failure | - | - |
| 10.22.E62 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{cases}0,&0 < b} | |
|
Error | Failure | - | Error |
| 10.22.E63 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\mu}@{at}\BesselJ{\mu-1}@{bt}\diff{t} = \begin{cases}b^{\mu-1}a^{-\mu},&0} | int(BesselJ(mu, a*t)*BesselJ(mu - 1, b*t), t = 0..infinity)= |
Integrate[BesselJ[\[Mu], a*t]*BesselJ[\[Mu]- 1, b*t], {t, 0, Infinity}]= |
Error | Failure | - | - |
| 10.22.E63 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{cases}b^{\mu-1}a^{-\mu},&0 < b} | |
|
Error | Failure | - | Error |
| 10.22.E63 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b < a,\\ (2b)^{-1},&b} | b < a ,(2*b)^(- 1), |
b < a ,(2*b)^(- 1), |
Error | Failure | - | Error |
| 10.22.E64 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\mu+2n+1}@{at}\BesselJ{\mu}@{bt}\diff{t} = \begin{cases}\dfrac{b^{\mu}\EulerGamma@{\mu+n+1}}{a^{\mu+1}n!}\hyperOlverF@{-n}{\mu+n+1}{\mu+1}{\dfrac{b^{2}}{a^{2}}},&0} | int(BesselJ(mu + 2*n + 1, a*t)*BesselJ(mu, b*t), t = 0..infinity)= |
Integrate[BesselJ[\[Mu]+ 2*n + 1, a*t]*BesselJ[\[Mu], b*t], {t, 0, Infinity}]= |
Error | Failure | - | - |
| 10.22.E64 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{cases}\dfrac{b^{\mu}\EulerGamma@{\mu+n+1}}{a^{\mu+1}n!}\hyperOlverF@{-n}{\mu+n+1}{\mu+1}{\dfrac{b^{2}}{a^{2}}},&0 < b} | |
|
Error | Failure | - | Error |
| 10.22.E64 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b < a,\\ (-1)^{n}/(2a),&b} | b < a ,(- 1)^(n)/(2*a), |
b < a ,(- 1)^(n)/(2*a), |
Error | Failure | - | Error |
| 10.22.E65 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{0}@{at}\left(\BesselJ{0}@{bt}-\BesselJ{0}@{ct}\right)\frac{\diff{t}}{t} = \begin{cases}0,&0} | int(BesselJ(0, a*t)*(BesselJ(0, b*t)- BesselJ(0, c*t))*(1)/(t), t = 0..infinity)= |
Integrate[BesselJ[0, a*t]*(BesselJ[0, b*t]- BesselJ[0, c*t])*Divide[1,t], {t, 0, Infinity}]= |
Failure | Failure | Error | - |
| 10.22.E65 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{cases}0,&0 <= b} | |
|
Failure | Failure | Error | - |
| 10.22.E65 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b < a,0} | b < a , 0 |
b < a , 0 |
Error | Failure | - | - |
| 10.22.E65 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a,0 < c} | a , 0 < c |
a , 0 < c |
Error | Failure | - | Error |
| 10.22.E65 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c <= a,\\ \ln@{c/a},&0} | c < = a , ln(c/ a), |
c < = a , Log[c/ a], |
Failure | Failure | Skip | Successful |
| 10.22.E66 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\BesselJ{\nu}@{bt}\BesselJ{\nu}@{ct}\diff{t} = \frac{1}{\pi(bc)^{\frac{1}{2}}}\*\assLegendreQ[]{\nu-\frac{1}{2}}@{\frac{a^{2}+b^{2}+c^{2}}{2bc}}} | int(exp(- a*t)*BesselJ(nu, b*t)*BesselJ(nu, c*t), t = 0..infinity)=(1)/(Pi*(b*c)^((1)/(2)))* LegendreQ(nu -(1)/(2), ((a)^(2)+ (b)^(2)+ (c)^(2))/(2*b*c)) |
Integrate[Exp[- a*t]*BesselJ[\[Nu], b*t]*BesselJ[\[Nu], c*t], {t, 0, Infinity}]=Divide[1,Pi*(b*c)^(Divide[1,2])]* LegendreQ[\[Nu]-Divide[1,2], 0, 3, Divide[(a)^(2)+ (b)^(2)+ (c)^(2),2*b*c]] |
Failure | Failure | Skip | Error |
| 10.22.E67 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t\exp@{-p^{2}t^{2}}\BesselJ{\nu}@{at}\BesselJ{\nu}@{bt}\diff{t} = \frac{1}{2p^{2}}\exp@{-\frac{a^{2}+b^{2}}{4p^{2}}}\modBesselI{\nu}\left(\frac{ab}{2p^{2}}\right)} | int(t*exp(- (p)^(2)* (t)^(2))*BesselJ(nu, a*t)*BesselJ(nu, b*t), t = 0..infinity)=(1)/(2*(p)^(2))*exp(-((a)^(2)+ (b)^(2))/(4*(p)^(2)))*BesselI(nu, (a*b)/(2*(p)^(2))) |
Integrate[t*Exp[- (p)^(2)* (t)^(2)]*BesselJ[\[Nu], a*t]*BesselJ[\[Nu], b*t], {t, 0, Infinity}]=Divide[1,2*(p)^(2)]*Exp[-Divide[(a)^(2)+ (b)^(2),4*(p)^(2)]]*BesselI[\[Nu], Divide[a*b,2*(p)^(2)]] |
Failure | Failure | Skip | Error |
| 10.22.E68 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t\exp@{-p^{2}t^{2}}\BesselJ{0}@{at}\BesselY{0}@{at}\diff{t} = -\frac{1}{2\pi p^{2}}\exp@{-\frac{a^{2}}{2p^{2}}}\modBesselK{0}\left(\frac{a^{2}}{2p^{2}}\right)} | int(t*exp(- (p)^(2)* (t)^(2))*BesselJ(0, a*t)*BesselY(0, a*t), t = 0..infinity)= -(1)/(2*Pi*(p)^(2))*exp(-((a)^(2))/(2*(p)^(2)))*BesselK(0, ((a)^(2))/(2*(p)^(2))) |
Integrate[t*Exp[- (p)^(2)* (t)^(2)]*BesselJ[0, a*t]*BesselY[0, a*t], {t, 0, Infinity}]= -Divide[1,2*Pi*(p)^(2)]*Exp[-Divide[(a)^(2),2*(p)^(2)]]*BesselK[0, Divide[(a)^(2),2*(p)^(2)]] |
Failure | Failure | Skip | Error |
| 10.22.E70 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselY{\nu}@{at}\BesselJ{\nu+1}@{bt}\frac{t\diff{t}}{t^{2}-z^{2}} = \frac{1}{2}\pi\BesselJ{\nu+1}@{bz}\HankelH{1}{\nu}@{az}} | int(BesselY(nu, a*t)*BesselJ(nu + 1, b*t)*(t)/((t)^(2)- (z)^(2)), t = 0..infinity)=(1)/(2)*Pi*BesselJ(nu + 1, b*z)*HankelH1(nu, a*z) |
Integrate[BesselY[\[Nu], a*t]*BesselJ[\[Nu]+ 1, b*t]*Divide[t,(t)^(2)- (z)^(2)], {t, 0, Infinity}]=Divide[1,2]*Pi*BesselJ[\[Nu]+ 1, b*z]*HankelH1[\[Nu], a*z] |
Failure | Failure | Skip | Error |
| 10.22.E71 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\mu}@{at}\BesselJ{\nu}@{bt}\BesselJ{\nu}@{ct}t^{1-\mu}\diff{t} = \frac{(bc)^{\mu-1}(\sin@@{\phi})^{\mu-\frac{1}{2}}}{(2\pi)^{\frac{1}{2}}a^{\mu}}\FerrersP[\frac{1}{2}-\mu]{\nu-\frac{1}{2}}(\cos@@{\phi})} | int(BesselJ(mu, a*t)*BesselJ(nu, b*t)*BesselJ(nu, c*t)*(t)^(1 - mu), t = 0..infinity)=((b*c)^(mu - 1)*(sin(phi))^(mu -(1)/(2)))/((2*Pi)^((1)/(2))* (a)^(mu))*LegendreP(nu -(1)/(2), (1)/(2)- mu, cos(phi)) |
Integrate[BesselJ[\[Mu], a*t]*BesselJ[\[Nu], b*t]*BesselJ[\[Nu], c*t]*(t)^(1 - \[Mu]), {t, 0, Infinity}]=Divide[(b*c)^(\[Mu]- 1)*(Sin[\[Phi]])^(\[Mu]-Divide[1,2]),(2*Pi)^(Divide[1,2])* (a)^(\[Mu])]*LegendreP[\[Nu]-Divide[1,2], Divide[1,2]- \[Mu], Cos[\[Phi]]] |
Failure | Failure | Skip | Skip |
| 10.22.E75 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselY{\nu}@{at}\BesselJ{\nu}@{bt}\BesselJ{\nu}@{ct}t^{1+\nu}\diff{t} = \begin{cases}-\dfrac{(abc)^{\nu}(-A)^{-\nu-\frac{1}{2}}}{\pi^{\frac{1}{2}}2^{\nu+1}\EulerGamma@{\frac{1}{2}-\nu}},&0} | int(BesselY(nu, a*t)*BesselJ(nu, b*t)*BesselJ(nu, c*t)*(t)^(1 + nu), t = 0..infinity)= |
Integrate[BesselY[\[Nu], a*t]*BesselJ[\[Nu], b*t]*BesselJ[\[Nu], c*t]*(t)^(1 + \[Nu]), {t, 0, Infinity}]= |
Error | Failure | - | - |
| 10.22.E75 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{cases}-\dfrac{(abc)^{\nu}(-A)^{-\nu-\frac{1}{2}}}{\pi^{\frac{1}{2}}2^{\nu+1}\EulerGamma@{\frac{1}{2}-\nu}},&0 < a} | |
|
Error | Failure | - | Error |
| 10.22.E75 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a < |b-c|,\\ 0,&|b-c|} | a <abs(b - c), 0 , |
a <Abs[b - c], 0 , |
Error | Failure | - | - |
| 10.23.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{0}^{2}@{z}+2\sum_{k=1}^{\infty}\BesselJ{k}^{2}@{z} = 1} | (BesselJ(0, z))^(2)+ 2*sum((BesselJ(k, z))^(2), k = 1..infinity)= 1 |
(BesselJ[0, z])^(2)+ 2*Sum[(BesselJ[k, z])^(2), {k, 1, Infinity}]= 1 |
Failure | Successful | Skip | - |
| 10.23.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=0}^{2n}(-1)^{k}\BesselJ{k}@{z}\BesselJ{2n-k}@{z}\\ +2\sum_{k=1}^{\infty}\BesselJ{k}@{z}\BesselJ{2n+k}@{z} = 0} | sum((- 1)^(k)* BesselJ(k, z)*BesselJ(2*n - k, z), k = 0..2*n)+ 2*sum(BesselJ(k, z)*BesselJ(2*n + k, z), k = 1..infinity)= 0 |
Sum[(- 1)^(k)* BesselJ[k, z]*BesselJ[2*n - k, z], {k, 0, 2*n}]+ 2*Sum[BesselJ[k, z]*BesselJ[2*n + k, z], {k, 1, Infinity}]= 0 |
Failure | Failure | Skip | Fail
Complex[4.242640687119286, 4.242640687119286] <- {Rule[n, 3], Rule[Sum[Times[BesselJ[k, z], BesselJ[Plus[k, Times[2, n]], z]], {k, 1, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[DifferenceRoot[Function[{, }, {Equal[Plus[Times[-1, Plus[-5, Times[-2, ], Times[2, n]], Power[z, 2], []], Times[Plus[-20, Times[-48, ], Times[-36, Power[, 2]], Times[-8, Power[, 3]], Times[48, n], Times[72, , n], Times[24, Power[, 2], n], Times[-16, Power[n, 2]], Times[-16, , Power[n, 2]], Times[-7, Power[z, 2]], Times[-2, , Power[z, 2]], Times[2, n, Power[z, 2]]], [Plus[1, ]]], Times[-2, Plus[-3, Times[-2, ], Times[2, n]], Plus[22, Times[24, ], Times[6, Power[, 2]], Times[-24, n], Times[-12, , n], Times[8, Power[n, 2]], Times[-1, Power[z, 2]]], [Plus[2, ]]], Times[2, Plus[-5, Times[-2, ], Times[2, n]], Plus[22, Times[24, ], Times[6, Power[, 2]], Times[-24, n], Times[-12, , n], Times[8, Power[n, 2]], Times[-1, Power[z, 2]]], [Plus[3, ]]], Times[Plus[108, Times[144, ], Times[60, Power[, 2]], Times[8, Power[, 3]], Times[-144, n], Times[-120, , n], Times[-24, Power[, 2], n], Times[48, Power[n, 2]], Times[16, , Power[n, 2]], Power[z, 2], Times[2, , Power[z, 2]], Times[-2, n, Power[z, 2]]], [Plus[4, ]]], Times[Plus[-3, Times[-2, ], Times[2, n]], Power[z, 2], [Plus[5, ]]]], 0], Equal[[0], 0], Equal[[1], Times[BesselJ[0, z], BesselJ[Times[2, n], z]]], Equal[[2], Plus[Times[BesselJ[0, z], BesselJ[Times[2, n], z]], Times[-1, BesselJ[1, z], BesselJ[Plus[-1, Times[2, n]], z]]]], Equal[[3], Plus[Times[BesselJ[0, z], BesselJ[Times[2, n], z]], Times[-1, BesselJ[1, z], BesselJ[Plus[-1, Times[2, n]], z]], Times[Power[z, -2], Plus[Times[-1, z, BesselJ[0, z]], Times[2, BesselJ[1, z]]], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]]]], Equal[[4], Plus[Times[BesselJ[0, z], BesselJ[Times[2, n], z]], Times[-1, BesselJ[1, z], BesselJ[Plus[-1, Times[2, n]], z]], Times[Power[z, -2], Plus[Times[-1, z, BesselJ[0, z]], Times[2, BesselJ[1, z]]], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]], Times[Power[z, -2], Plus[Times[z, BesselJ[1, z]], Times[-4, Power[z, -1], Plus[Times[-1, z, BesselJ[0, z]], Times[2, BesselJ[1, z]]]]], Plus[Times[-1, z, BesselJ[Plus[-1, Times[2, n]], z]], Times[-4, Power[z, -1], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]], Times[4, n, Power[z, -1], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]]]]]]}]][Plus[1, Times[2, n]]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.242640687119286, 1.4142135623730951] <- {Rule[n, 3], Rule[Sum[Times[BesselJ[k, z], BesselJ[Plus[k, Times[2, n]], z]], {k, 1, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[DifferenceRoot[Function[{, }, {Equal[Plus[Times[-1, Plus[-5, Times[-2, ], Times[2, n]], Power[z, 2], []], Times[Plus[-20, Times[-48, ], Times[-36, Power[, 2]], Times[-8, Power[, 3]], Times[48, n], Times[72, , n], Times[24, Power[, 2], n], Times[-16, Power[n, 2]], Times[-16, , Power[n, 2]], Times[-7, Power[z, 2]], Times[-2, , Power[z, 2]], Times[2, n, Power[z, 2]]], [Plus[1, ]]], Times[-2, Plus[-3, Times[-2, ], Times[2, n]], Plus[22, Times[24, ], Times[6, Power[, 2]], Times[-24, n], Times[-12, , n], Times[8, Power[n, 2]], Times[-1, Power[z, 2]]], [Plus[2, ]]], Times[2, Plus[-5, Times[-2, ], Times[2, n]], Plus[22, Times[24, ], Times[6, Power[, 2]], Times[-24, n], Times[-12, , n], Times[8, Power[n, 2]], Times[-1, Power[z, 2]]], [Plus[3, ]]], Times[Plus[108, Times[144, ], Times[60, Power[, 2]], Times[8, Power[, 3]], Times[-144, n], Times[-120, , n], Times[-24, Power[, 2], n], Times[48, Power[n, 2]], Times[16, , Power[n, 2]], Power[z, 2], Times[2, , Power[z, 2]], Times[-2, n, Power[z, 2]]], [Plus[4, ]]], Times[Plus[-3, Times[-2, ], Times[2, n]], Power[z, 2], [Plus[5, ]]]], 0], Equal[[0], 0], Equal[[1], Times[BesselJ[0, z], BesselJ[Times[2, n], z]]], Equal[[2], Plus[Times[BesselJ[0, z], BesselJ[Times[2, n], z]], Times[-1, BesselJ[1, z], BesselJ[Plus[-1, Times[2, n]], z]]]], Equal[[3], Plus[Times[BesselJ[0, z], BesselJ[Times[2, n], z]], Times[-1, BesselJ[1, z], BesselJ[Plus[-1, Times[2, n]], z]], Times[Power[z, -2], Plus[Times[-1, z, BesselJ[0, z]], Times[2, BesselJ[1, z]]], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]]]], Equal[[4], Plus[Times[BesselJ[0, z], BesselJ[Times[2, n], z]], Times[-1, BesselJ[1, z], BesselJ[Plus[-1, Times[2, n]], z]], Times[Power[z, -2], Plus[Times[-1, z, BesselJ[0, z]], Times[2, BesselJ[1, z]]], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]], Times[Power[z, -2], Plus[Times[z, BesselJ[1, z]], Times[-4, Power[z, -1], Plus[Times[-1, z, BesselJ[0, z]], Times[2, BesselJ[1, z]]]]], Plus[Times[-1, z, BesselJ[Plus[-1, Times[2, n]], z]], Times[-4, Power[z, -1], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]], Times[4, n, Power[z, -1], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]]]]]]}]][Plus[1, Times[2, n]]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[n, 3], Rule[Sum[Times[BesselJ[k, z], BesselJ[Plus[k, Times[2, n]], z]], {k, 1, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[DifferenceRoot[Function[{, }, {Equal[Plus[Times[-1, Plus[-5, Times[-2, ], Times[2, n]], Power[z, 2], []], Times[Plus[-20, Times[-48, ], Times[-36, Power[, 2]], Times[-8, Power[, 3]], Times[48, n], Times[72, , n], Times[24, Power[, 2], n], Times[-16, Power[n, 2]], Times[-16, , Power[n, 2]], Times[-7, Power[z, 2]], Times[-2, , Power[z, 2]], Times[2, n, Power[z, 2]]], [Plus[1, ]]], Times[-2, Plus[-3, Times[-2, ], Times[2, n]], Plus[22, Times[24, ], Times[6, Power[, 2]], Times[-24, n], Times[-12, , n], Times[8, Power[n, 2]], Times[-1, Power[z, 2]]], [Plus[2, ]]], Times[2, Plus[-5, Times[-2, ], Times[2, n]], Plus[22, Times[24, ], Times[6, Power[, 2]], Times[-24, n], Times[-12, , n], Times[8, Power[n, 2]], Times[-1, Power[z, 2]]], [Plus[3, ]]], Times[Plus[108, Times[144, ], Times[60, Power[, 2]], Times[8, Power[, 3]], Times[-144, n], Times[-120, , n], Times[-24, Power[, 2], n], Times[48, Power[n, 2]], Times[16, , Power[n, 2]], Power[z, 2], Times[2, , Power[z, 2]], Times[-2, n, Power[z, 2]]], [Plus[4, ]]], Times[Plus[-3, Times[-2, ], Times[2, n]], Power[z, 2], [Plus[5, ]]]], 0], Equal[[0], 0], Equal[[1], Times[BesselJ[0, z], BesselJ[Times[2, n], z]]], Equal[[2], Plus[Times[BesselJ[0, z], BesselJ[Times[2, n], z]], Times[-1, BesselJ[1, z], BesselJ[Plus[-1, Times[2, n]], z]]]], Equal[[3], Plus[Times[BesselJ[0, z], BesselJ[Times[2, n], z]], Times[-1, BesselJ[1, z], BesselJ[Plus[-1, Times[2, n]], z]], Times[Power[z, -2], Plus[Times[-1, z, BesselJ[0, z]], Times[2, BesselJ[1, z]]], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]]]], Equal[[4], Plus[Times[BesselJ[0, z], BesselJ[Times[2, n], z]], Times[-1, BesselJ[1, z], BesselJ[Plus[-1, Times[2, n]], z]], Times[Power[z, -2], Plus[Times[-1, z, BesselJ[0, z]], Times[2, BesselJ[1, z]]], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]], Times[Power[z, -2], Plus[Times[z, BesselJ[1, z]], Times[-4, Power[z, -1], Plus[Times[-1, z, BesselJ[0, z]], Times[2, BesselJ[1, z]]]]], Plus[Times[-1, z, BesselJ[Plus[-1, Times[2, n]], z]], Times[-4, Power[z, -1], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]], Times[4, n, Power[z, -1], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]]]]]]}]][Plus[1, Times[2, n]]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, 4.242640687119286] <- {Rule[n, 3], Rule[Sum[Times[BesselJ[k, z], BesselJ[Plus[k, Times[2, n]], z]], {k, 1, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[DifferenceRoot[Function[{, }, {Equal[Plus[Times[-1, Plus[-5, Times[-2, ], Times[2, n]], Power[z, 2], []], Times[Plus[-20, Times[-48, ], Times[-36, Power[, 2]], Times[-8, Power[, 3]], Times[48, n], Times[72, , n], Times[24, Power[, 2], n], Times[-16, Power[n, 2]], Times[-16, , Power[n, 2]], Times[-7, Power[z, 2]], Times[-2, , Power[z, 2]], Times[2, n, Power[z, 2]]], [Plus[1, ]]], Times[-2, Plus[-3, Times[-2, ], Times[2, n]], Plus[22, Times[24, ], Times[6, Power[, 2]], Times[-24, n], Times[-12, , n], Times[8, Power[n, 2]], Times[-1, Power[z, 2]]], [Plus[2, ]]], Times[2, Plus[-5, Times[-2, ], Times[2, n]], Plus[22, Times[24, ], Times[6, Power[, 2]], Times[-24, n], Times[-12, , n], Times[8, Power[n, 2]], Times[-1, Power[z, 2]]], [Plus[3, ]]], Times[Plus[108, Times[144, ], Times[60, Power[, 2]], Times[8, Power[, 3]], Times[-144, n], Times[-120, , n], Times[-24, Power[, 2], n], Times[48, Power[n, 2]], Times[16, , Power[n, 2]], Power[z, 2], Times[2, , Power[z, 2]], Times[-2, n, Power[z, 2]]], [Plus[4, ]]], Times[Plus[-3, Times[-2, ], Times[2, n]], Power[z, 2], [Plus[5, ]]]], 0], Equal[[0], 0], Equal[[1], Times[BesselJ[0, z], BesselJ[Times[2, n], z]]], Equal[[2], Plus[Times[BesselJ[0, z], BesselJ[Times[2, n], z]], Times[-1, BesselJ[1, z], BesselJ[Plus[-1, Times[2, n]], z]]]], Equal[[3], Plus[Times[BesselJ[0, z], BesselJ[Times[2, n], z]], Times[-1, BesselJ[1, z], BesselJ[Plus[-1, Times[2, n]], z]], Times[Power[z, -2], Plus[Times[-1, z, BesselJ[0, z]], Times[2, BesselJ[1, z]]], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]]]], Equal[[4], Plus[Times[BesselJ[0, z], BesselJ[Times[2, n], z]], Times[-1, BesselJ[1, z], BesselJ[Plus[-1, Times[2, n]], z]], Times[Power[z, -2], Plus[Times[-1, z, BesselJ[0, z]], Times[2, BesselJ[1, z]]], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]], Times[Power[z, -2], Plus[Times[z, BesselJ[1, z]], Times[-4, Power[z, -1], Plus[Times[-1, z, BesselJ[0, z]], Times[2, BesselJ[1, z]]]]], Plus[Times[-1, z, BesselJ[Plus[-1, Times[2, n]], z]], Times[-4, Power[z, -1], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]], Times[4, n, Power[z, -1], Plus[Times[-1, z, BesselJ[Times[2, n], z]], Times[-2, BesselJ[Plus[-1, Times[2, n]], z]], Times[4, n, BesselJ[Plus[-1, Times[2, n]], z]]]]]]]]}]][Plus[1, Times[2, n]]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.23.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=0}^{n}\BesselJ{k}@{z}\BesselJ{n-k}@{z}+2\sum_{k=1}^{\infty}(-1)^{k}\BesselJ{k}@{z}\BesselJ{n+k}@{z} = \BesselJ{n}@{2z}} | sum(BesselJ(k, z)*BesselJ(n - k, z), k = 0..n)+ 2*sum((- 1)^(k)* BesselJ(k, z)*BesselJ(n + k, z), k = 1..infinity)= BesselJ(n, 2*z) |
Sum[BesselJ[k, z]*BesselJ[n - k, z], {k, 0, n}]+ 2*Sum[(- 1)^(k)* BesselJ[k, z]*BesselJ[n + k, z], {k, 1, Infinity}]= BesselJ[n, 2*z] |
Failure | Failure | Skip | Skip |
| 10.23#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \sqrt{u^{2}+v^{2}-2uv\cos@@{\alpha}}} | w =sqrt((u)^(2)+ (v)^(2)- 2*u*v*cos(alpha)) |
w =Sqrt[(u)^(2)+ (v)^(2)- 2*u*v*Cos[\[Alpha]]] |
Failure | Failure | Fail .7483404465-2.552464124*I <- {alpha = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)}.7483404465-5.380891248*I <- {alpha = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)}-2.080086678-5.380891248*I <- {alpha = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)}-2.080086678-2.552464124*I <- {alpha = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Skip |
| 10.23#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u-v\cos@@{\alpha} = w\cos@@{\chi}} | u - v*cos(alpha)= w*cos(chi) |
u - v*Cos[\[Alpha]]= w*Cos[\[Chi]] |
Failure | Failure | Skip | Skip |
| 10.23#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle v\sin@@{\alpha} = w\sin@@{\chi}} | v*sin(alpha)= w*sin(chi) |
v*Sin[\[Alpha]]= w*Sin[\[Chi]] |
Failure | Failure | Fail -.853510328+6.085461480*I <- {alpha = 2^(1/2)+I*2^(1/2), chi = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)}5.231951152+6.938971808*I <- {alpha = 2^(1/2)+I*2^(1/2), chi = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)}6.085461480+.853510328*I <- {alpha = 2^(1/2)+I*2^(1/2), chi = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)}.853510328-6.085461480*I <- {alpha = 2^(1/2)+I*2^(1/2), chi = 2^(1/2)+I*2^(1/2), v = 2^(1/2)-I*2^(1/2), w = 2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-0.853510326577255, 0.853510326577255] <- {Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.231951158402261, 6.938971811556771] <- {Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.085461484979516, 6.085461484979516] <- {Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.853510326577255, -0.853510326577255] <- {Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.23.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{iv\cos@@{\alpha}} = \frac{\EulerGamma@{\nu}}{(\tfrac{1}{2}v)^{\nu}}\*\sum_{k=0}^{\infty}(\nu+k)i^{k}\BesselJ{\nu+k}@{v}\ultrasphpoly{\nu}{k}@{\cos@@{\alpha}}} | exp(I*v*cos(alpha))=(GAMMA(nu))/(((1)/(2)*v)^(nu))* sum((nu + k)* (I)^(k)* BesselJ(nu + k, v)*GegenbauerC(k, nu, cos(alpha)), k = 0..infinity) |
Exp[I*v*Cos[\[Alpha]]]=Divide[Gamma[\[Nu]],(Divide[1,2]*v)^(\[Nu])]* Sum[(\[Nu]+ k)* (I)^(k)* BesselJ[\[Nu]+ k, v]*GegenbauerC[k, \[Nu], Cos[\[Alpha]]], {k, 0, Infinity}] |
Error | Failure | - | Skip |
| 10.23.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\tfrac{1}{2}z)^{\nu} = \sum_{k=0}^{\infty}\frac{(\nu+2k)\EulerGamma@{\nu+k}}{k!}\BesselJ{\nu+2k}@{z}} | ((1)/(2)*z)^(nu)= sum(((nu + 2*k)* GAMMA(nu + k))/(factorial(k))*BesselJ(nu + 2*k, z), k = 0..infinity) |
(Divide[1,2]*z)^(\[Nu])= Sum[Divide[(\[Nu]+ 2*k)* Gamma[\[Nu]+ k],(k)!]*BesselJ[\[Nu]+ 2*k, z], {k, 0, Infinity}] |
Failure | Successful | Skip | - |
| 10.23.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{0}@{z} = \frac{2}{\pi}\left(\ln@{\tfrac{1}{2}z}+\EulerConstant\right)\BesselJ{0}@{z}-\frac{4}{\pi}\sum_{k=1}^{\infty}(-1)^{k}\frac{\BesselJ{2k}@{z}}{k}} | BesselY(0, z)=(2)/(Pi)*(ln((1)/(2)*z)+ gamma)* BesselJ(0, z)-(4)/(Pi)*sum((- 1)^(k)*(BesselJ(2*k, z))/(k), k = 1..infinity) |
BesselY[0, z]=Divide[2,Pi]*(Log[Divide[1,2]*z]+ EulerGamma)* BesselJ[0, z]-Divide[4,Pi]*Sum[(- 1)^(k)*Divide[BesselJ[2*k, z],k], {k, 1, Infinity}] |
Failure | Successful | Skip | - |
| 10.23.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{n}@{z} = -\frac{n!(\tfrac{1}{2}z)^{-n}}{\pi}\sum_{k=0}^{n-1}\frac{(\tfrac{1}{2}z)^{k}\BesselJ{k}@{z}}{k!(n-k)}+\frac{2}{\pi}\left(\ln@{\tfrac{1}{2}z}-\digamma@{n+1}\right)\BesselJ{n}@{z}-\frac{2}{\pi}\sum_{k=1}^{\infty}(-1)^{k}\frac{(n+2k)\BesselJ{n+2k}@{z}}{k(n+k)}} | BesselY(n, z)= -(factorial(n)*((1)/(2)*z)^(- n))/(Pi)*sum((((1)/(2)*z)^(k)* BesselJ(k, z))/(factorial(k)*(n - k)), k = 0..n - 1)+(2)/(Pi)*(ln((1)/(2)*z)- Psi(n + 1))* BesselJ(n, z)-(2)/(Pi)*sum((- 1)^(k)*((n + 2*k)* BesselJ(n + 2*k, z))/(k*(n + k)), k = 1..infinity) |
BesselY[n, z]= -Divide[(n)!*(Divide[1,2]*z)^(- n),Pi]*Sum[Divide[(Divide[1,2]*z)^(k)* BesselJ[k, z],(k)!*(n - k)], {k, 0, n - 1}]+Divide[2,Pi]*(Log[Divide[1,2]*z]- PolyGamma[n + 1])* BesselJ[n, z]-Divide[2,Pi]*Sum[(- 1)^(k)*Divide[(n + 2*k)* BesselJ[n + 2*k, z],k*(n + k)], {k, 1, Infinity}] |
Failure | Failure | Skip | Successful |
| 10.24.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{2}\deriv[2]{w}{x}+x\deriv{w}{x}+(x^{2}+\nu^{2})w = 0} | (x)^(2)* diff(w, [x$(2)])+ x*diff(w, x)+((x)^(2)+ (nu)^(2))* w = 0 |
(x)^(2)* D[w, {x, 2}]+ x*D[w, x]+((x)^(2)+ (\[Nu])^(2))* w = 0 |
Failure | Failure | Fail -4.242640683+7.071067807*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), x = 1}.2828427124e-8+11.31370849*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), x = 2}7.071067813+18.38477630*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), x = 3}7.071067807+4.242640683*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[-4.242640687119286, 7.0710678118654755] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, 11.313708498984761] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[7.0710678118654755, 18.38477631085024] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[7.0710678118654755, -4.242640687119286] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.24#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJimag{\nu}@{x} = \sech@{\tfrac{1}{2}\pi\nu}\realpart@@{(\BesselJ{i\nu}@{x})}} | sech((1/2)*Pi*(nu))*Re(BesselJ(I*(nu), x))= sech((1)/(2)*Pi*nu)*Re(BesselJ(I*nu, x)) |
Sech[1/2 Pi \[Nu]] Re[BesselJ[I \[Nu], x]]= Sech[Divide[1,2]*Pi*\[Nu]]*Re[BesselJ[I*\[Nu], x]] |
Successful | Successful | - | - |
| 10.24#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselYimag{\nu}@{x} = \sech@{\tfrac{1}{2}\pi\nu}\realpart@@{(\BesselY{i\nu}@{x})}} | sech((1/2)*Pi*(nu))*Re(BesselY(I*(nu), x))= sech((1)/(2)*Pi*nu)*Re(BesselY(I*nu, x)) |
Sech[1/2 Pi \[Nu]] Re[BesselY[I \[Nu], x]]= Sech[Divide[1,2]*Pi*\[Nu]]*Re[BesselY[I*\[Nu], x]] |
Successful | Successful | - | - |
| 10.24.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{1+i\nu} = \left(\frac{\pi\nu}{\sinh@{\pi\nu}}\right)^{\frac{1}{2}}e^{i\gamma_{\nu}}} | GAMMA(1 + I*nu)=((Pi*nu)/(sinh(Pi*nu)))^((1)/(2))* exp(I*gamma[nu]) |
Gamma[1 + I*\[Nu]]=(Divide[Pi*\[Nu],Sinh[Pi*\[Nu]]])^(Divide[1,2])* Exp[I*Subscript[\[Gamma], \[Nu]]] |
Failure | Failure | Fail -.7864250629e-1-.1325922997*I <- {nu = 2^(1/2)+I*2^(1/2), gamma[nu] = 2^(1/2)+I*2^(1/2)}1.283131241-.7318661334*I <- {nu = 2^(1/2)+I*2^(1/2), gamma[nu] = 2^(1/2)-I*2^(1/2)}-1.737329775+.6511700055e-1*I <- {nu = 2^(1/2)+I*2^(1/2), gamma[nu] = -2^(1/2)-I*2^(1/2)}-.2571691098-.8548601655e-1*I <- {nu = 2^(1/2)+I*2^(1/2), gamma[nu] = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Successful |
| 10.24#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJimag{-\nu}@{x} = \BesselJimag{\nu}@{x}} | sech((1/2)*Pi*(- nu))*Re(BesselJ(I*(- nu), x))= sech((1/2)*Pi*(nu))*Re(BesselJ(I*(nu), x)) |
Sech[1/2 Pi - \[Nu]] Re[BesselJ[I - \[Nu], x]]= Sech[1/2 Pi \[Nu]] Re[BesselJ[I \[Nu], x]] |
Failure | Failure | Fail -.4072055387-.5224985000*I <- {nu = 2^(1/2)+I*2^(1/2), x = 1}-.9080795132-1.165185978*I <- {nu = 2^(1/2)+I*2^(1/2), x = 2}-.3702824234-.4751212654*I <- {nu = 2^(1/2)+I*2^(1/2), x = 3}.4072055387-.5224985000*I <- {nu = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[-5.717128116473797, -5.753336678220267] <- {Rule[x, 1], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.18027157410826, -3.3753924459653097] <- {Rule[x, 2], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.3142029624806735, -0.37398699406023267] <- {Rule[x, 3], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[335.05864396153805, -329.61926001758485] <- {Rule[x, 1], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.24#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselYimag{-\nu}@{x} = \BesselYimag{\nu}@{x}} | sech((1/2)*Pi*(- nu))*Re(BesselY(I*(- nu), x))= sech((1/2)*Pi*(nu))*Re(BesselY(I*(nu), x)) |
Sech[1/2 Pi - \[Nu]] Re[BesselY[I - \[Nu], x]]= Sech[1/2 Pi \[Nu]] Re[BesselY[I \[Nu], x]] |
Failure | Failure | Fail 1.996706293+2.562037949*I <- {nu = 2^(1/2)+I*2^(1/2), x = 1}.9116896387e-1+.1169818245*I <- {nu = 2^(1/2)+I*2^(1/2), x = 2}-.4855048259-.6229668292*I <- {nu = 2^(1/2)+I*2^(1/2), x = 3}-1.996706293+2.562037949*I <- {nu = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[3.2898455559215325, 3.8112807679993184] <- {Rule[x, 1], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6593720309671711, -1.6388399049382785] <- {Rule[x, 2], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.5986068001960096, -2.7005355423537045] <- {Rule[x, 3], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[104.18379750674467, -102.47171282147995] <- {Rule[x, 1], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.24.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselYimag{0}@{x} = \BesselY{0}@{x}} | sech((1/2)*Pi*(0))*Re(BesselY(I*(0), x))= BesselY(0, x) |
Sech[1/2 Pi 0] Re[BesselY[I 0, x]]= BesselY[0, x] |
Failure | Failure | Successful | Successful |
| 10.25.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{2}\deriv[2]{w}{z}+z\deriv{w}{z}-(z^{2}+\nu^{2})w = 0} | (z)^(2)* diff(w, [z$(2)])+ z*diff(w, z)-((z)^(2)+ (nu)^(2))* w = 0 |
(z)^(2)* D[w, {z, 2}]+ z*D[w, z]-((z)^(2)+ (\[Nu])^(2))* w = 0 |
Failure | Failure | Fail 11.31370849-11.31370849*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}11.31370849-11.31370849*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-11.31370849-11.31370849*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-11.31370849-11.31370849*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}... skip entries to safe data |
Fail
Complex[11.313708498984761, -11.313708498984761] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[11.313708498984761, -11.313708498984761] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-11.313708498984761, 11.313708498984761] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-11.313708498984761, 11.313708498984761] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.25.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = (\tfrac{1}{2}z)^{\nu}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}}} | BesselI(nu, z)=((1)/(2)*z)^(nu)* sum((((1)/(4)*(z)^(2))^(k))/(factorial(k)*GAMMA(nu + k + 1)), k = 0..infinity) |
BesselI[\[Nu], z]=(Divide[1,2]*z)^(\[Nu])* Sum[Divide[(Divide[1,4]*(z)^(2))^(k),(k)!*Gamma[\[Nu]+ k + 1]], {k, 0, Infinity}] |
Successful | Successful | - | - |
| 10.27.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{-n}@{z} = \modBesselI{n}@{z}} | BesselI(- n, z)= BesselI(n, z) |
BesselI[- n, z]= BesselI[n, z] |
Failure | Failure | Successful | Successful |
| 10.27.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{-\nu}@{z} = \modBesselI{\nu}@{z}+(2/\pi)\sin@{\nu\pi}\modBesselK{\nu}@{z}} | BesselI(- nu, z)= BesselI(nu, z)+(2/ Pi)* sin(nu*Pi)*BesselK(nu, z) |
BesselI[- \[Nu], z]= BesselI[\[Nu], z]+(2/ Pi)* Sin[\[Nu]*Pi]*BesselK[\[Nu], z] |
Successful | Successful | - | - |
| 10.27.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{-\nu}@{z} = \modBesselK{\nu}@{z}} | BesselK(- nu, z)= BesselK(nu, z) |
BesselK[- \[Nu], z]= BesselK[\[Nu], z] |
Successful | Successful | - | - |
| 10.27.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \tfrac{1}{2}\pi\frac{\modBesselI{-\nu}@{z}-\modBesselI{\nu}@{z}}{\sin@{\nu\pi}}} | BesselK(nu, z)=(1)/(2)*Pi*(BesselI(- nu, z)- BesselI(nu, z))/(sin(nu*Pi)) |
BesselK[\[Nu], z]=Divide[1,2]*Pi*Divide[BesselI[- \[Nu], z]- BesselI[\[Nu], z],Sin[\[Nu]*Pi]] |
Successful | Successful | - | - |
| 10.27.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = e^{-\nu\pi i/2}\BesselJ{\nu}@{ze^{+\pi i/2}}} | BesselI(nu, z)= exp(- nu*Pi*I/ 2)*BesselJ(nu, z*exp(+ Pi*I/ 2)) |
BesselI[\[Nu], z]= Exp[- \[Nu]*Pi*I/ 2]*BesselJ[\[Nu], z*Exp[+ Pi*I/ 2]] |
Failure | Failure | Error | Error |
| 10.27.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = e^{+\nu\pi i/2}\BesselJ{\nu}@{ze^{-\pi i/2}}} | BesselI(nu, z)= exp(+ nu*Pi*I/ 2)*BesselJ(nu, z*exp(- Pi*I/ 2)) |
BesselI[\[Nu], z]= Exp[+ \[Nu]*Pi*I/ 2]*BesselJ[\[Nu], z*Exp[- Pi*I/ 2]] |
Failure | Failure | Error | Error |
| 10.27.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \tfrac{1}{2}e^{-\nu\pi i/2}\left(\HankelH{1}{\nu}@{ze^{+\pi i/2}}+\HankelH{2}{\nu}@{ze^{+\pi i/2}}\right)} | BesselI(nu, z)=(1)/(2)*exp(- nu*Pi*I/ 2)*(HankelH1(nu, z*exp(+ Pi*I/ 2))+ HankelH2(nu, z*exp(+ Pi*I/ 2))) |
BesselI[\[Nu], z]=Divide[1,2]*Exp[- \[Nu]*Pi*I/ 2]*(HankelH1[\[Nu], z*Exp[+ Pi*I/ 2]]+ HankelH2[\[Nu], z*Exp[+ Pi*I/ 2]]) |
Failure | Failure | Error | Error |
| 10.27.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \tfrac{1}{2}e^{+\nu\pi i/2}\left(\HankelH{1}{\nu}@{ze^{-\pi i/2}}+\HankelH{2}{\nu}@{ze^{-\pi i/2}}\right)} | BesselI(nu, z)=(1)/(2)*exp(+ nu*Pi*I/ 2)*(HankelH1(nu, z*exp(- Pi*I/ 2))+ HankelH2(nu, z*exp(- Pi*I/ 2))) |
BesselI[\[Nu], z]=Divide[1,2]*Exp[+ \[Nu]*Pi*I/ 2]*(HankelH1[\[Nu], z*Exp[- Pi*I/ 2]]+ HankelH2[\[Nu], z*Exp[- Pi*I/ 2]]) |
Failure | Failure | Error | Error |
| 10.27.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \begin{cases}\tfrac{1}{2}\pi ie^{\nu\pi i/2}\HankelH{1}{\nu}@{ze^{\pi i/2}},&-\pi} | BesselK(nu, z)= |
BesselK[\[Nu], z]= |
Error | Failure | - | - |
| 10.27.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{cases}\tfrac{1}{2}\pi ie^{\nu\pi i/2}\HankelH{1}{\nu}@{ze^{\pi i/2}},&-\pi <= \phase@@{z}} | |
|
Error | Failure | - | Error |
| 10.27.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pi i\BesselJ{\nu}@{z} = e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}-e^{\nu\pi i/2}\modBesselK{\nu}@{ze^{\pi i/2}}} | Pi*I*BesselJ(nu, z)= exp(- nu*Pi*I/ 2)*BesselK(nu, z*exp(- Pi*I/ 2))- exp(nu*Pi*I/ 2)*BesselK(nu, z*exp(Pi*I/ 2)) |
Pi*I*BesselJ[\[Nu], z]= Exp[- \[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[- Pi*I/ 2]]- Exp[\[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[Pi*I/ 2]] |
Failure | Failure | Skip | Successful |
| 10.27.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\pi\BesselY{\nu}@{z} = e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}+e^{\nu\pi i/2}\modBesselK{\nu}@{ze^{\pi i/2}}} | - Pi*BesselY(nu, z)= exp(- nu*Pi*I/ 2)*BesselK(nu, z*exp(- Pi*I/ 2))+ exp(nu*Pi*I/ 2)*BesselK(nu, z*exp(Pi*I/ 2)) |
- Pi*BesselY[\[Nu], z]= Exp[- \[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[- Pi*I/ 2]]+ Exp[\[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[Pi*I/ 2]] |
Failure | Failure | Skip | Successful |
| 10.27.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = e^{+(\nu+1)\pi i/2}\modBesselI{\nu}@{ze^{-\pi i/2}}-(2/\pi)e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}} | BesselY(nu, z)= exp(+(nu + 1)* Pi*I/ 2)*BesselI(nu, z*exp(- Pi*I/ 2))-(2/ Pi)* exp(- nu*Pi*I/ 2)*BesselK(nu, z*exp(- Pi*I/ 2)) |
BesselY[\[Nu], z]= Exp[+(\[Nu]+ 1)* Pi*I/ 2]*BesselI[\[Nu], z*Exp[- Pi*I/ 2]]-(2/ Pi)* Exp[- \[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[- Pi*I/ 2]] |
Failure | Failure | Error | Error |
| 10.27.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = e^{-(\nu+1)\pi i/2}\modBesselI{\nu}@{ze^{+\pi i/2}}-(2/\pi)e^{+\nu\pi i/2}\modBesselK{\nu}@{ze^{+\pi i/2}}} | BesselY(nu, z)= exp(-(nu + 1)* Pi*I/ 2)*BesselI(nu, z*exp(+ Pi*I/ 2))-(2/ Pi)* exp(+ nu*Pi*I/ 2)*BesselK(nu, z*exp(+ Pi*I/ 2)) |
BesselY[\[Nu], z]= Exp[-(\[Nu]+ 1)* Pi*I/ 2]*BesselI[\[Nu], z*Exp[+ Pi*I/ 2]]-(2/ Pi)* Exp[+ \[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[+ Pi*I/ 2]] |
Failure | Failure | Error | Error |
| 10.28.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modBesselI{\nu}@{z},\modBesselI{-\nu}@{z}} = \modBesselI{\nu}@{z}\modBesselI{-\nu-1}@{z}-\modBesselI{\nu+1}@{z}\modBesselI{-\nu}@{z}} | (BesselI(nu, z))*diff(BesselI(- nu, z), x)-diff(BesselI(nu, z), x)*(BesselI(- nu, z))= BesselI(nu, z)*BesselI(- nu - 1, z)- BesselI(nu + 1, z)*BesselI(- nu, z) |
Wronskian[{BesselI[\[Nu], z], BesselI[- \[Nu], z]}, x]= BesselI[\[Nu], z]*BesselI[- \[Nu]- 1, z]- BesselI[\[Nu]+ 1, z]*BesselI[- \[Nu], z] |
Failure | Failure | Fail -11.77116916+6.676770606*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-6.676770612-11.77116916*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}11.77116916-6.676770609*I <- {nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}6.676770609+11.77116916*I <- {nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-11.771169167436858, 6.676770630088813] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-6.676770630088807, 11.771169167436854] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[11.771169167436858, -6.676770630088829] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.67677063008883, -11.771169167436856] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.28.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z}\modBesselI{-\nu-1}@{z}-\modBesselI{\nu+1}@{z}\modBesselI{-\nu}@{z} = -2\sin@{\nu\pi}/(\pi z)} | BesselI(nu, z)*BesselI(- nu - 1, z)- BesselI(nu + 1, z)*BesselI(- nu, z)= - 2*sin(nu*Pi)/(Pi*z) |
BesselI[\[Nu], z]*BesselI[- \[Nu]- 1, z]- BesselI[\[Nu]+ 1, z]*BesselI[- \[Nu], z]= - 2*Sin[\[Nu]*Pi]/(Pi*z) |
Failure | Successful | Successful | - |
| 10.28.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modBesselK{\nu}@{z},\modBesselI{\nu}@{z}} = \modBesselI{\nu}@{z}\modBesselK{\nu+1}@{z}+\modBesselI{\nu+1}@{z}\modBesselK{\nu}@{z}} | (BesselK(nu, z))*diff(BesselI(nu, z), x)-diff(BesselK(nu, z), x)*(BesselI(nu, z))= BesselI(nu, z)*BesselK(nu + 1, z)+ BesselI(nu + 1, z)*BesselK(nu, z) |
Wronskian[{BesselK[\[Nu], z], BesselI[\[Nu], z]}, x]= BesselI[\[Nu], z]*BesselK[\[Nu]+ 1, z]+ BesselI[\[Nu]+ 1, z]*BesselK[\[Nu], z] |
Failure | Failure | Fail -.3535533907+.3535533906*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-.3535533908-.3535533907*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}.353553388-.35355339*I <- {nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}.3535533905+.3535533907*I <- {nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-0.35355339059327384, 0.3535533905932732] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.35355339059327306, 0.3535533905932739] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.35355339059327395, 0.35355339059327373] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.3535533905932736, 0.3535533905932738] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.28.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z}\modBesselK{\nu+1}@{z}+\modBesselI{\nu+1}@{z}\modBesselK{\nu}@{z} = 1/z} | BesselI(nu, z)*BesselK(nu + 1, z)+ BesselI(nu + 1, z)*BesselK(nu, z)= 1/ z |
BesselI[\[Nu], z]*BesselK[\[Nu]+ 1, z]+ BesselI[\[Nu]+ 1, z]*BesselK[\[Nu], z]= 1/ z |
Failure | Successful | Successful | - |
| 10.29#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{0}'@{z} = \modBesselI{1}@{z}} | subs( temp=z, diff( BesselI(0, temp), temp$(1) ) )= BesselI(1, z) |
(D[BesselI[0, temp], {temp, 1}]/.temp-> z)= BesselI[1, z] |
Successful | Successful | - | - |
| 10.29#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{0}'@{z} = -\modBesselK{1}@{z}} | subs( temp=z, diff( BesselK(0, temp), temp$(1) ) )= - BesselK(1, z) |
(D[BesselK[0, temp], {temp, 1}]/.temp-> z)= - BesselK[1, z] |
Successful | Successful | - | - |
| 10.31.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{n}@{z} = \tfrac{1}{2}(\tfrac{1}{2}z)^{-n}\sum_{k=0}^{n-1}\frac{(n-k-1)!}{k!}(-\tfrac{1}{4}z^{2})^{k}+(-1)^{n+1}\ln@{\tfrac{1}{2}z}\modBesselI{n}@{z}+(-1)^{n}\tfrac{1}{2}(\tfrac{1}{2}z)^{n}\sum_{k=0}^{\infty}\left(\digamma@{k+1}+\digamma@{n+k+1}\right)\frac{(\tfrac{1}{4}z^{2})^{k}}{k!(n+k)!}} | BesselK(n, z)=(1)/(2)*((1)/(2)*z)^(- n)* sum((factorial(n - k - 1))/(factorial(k))*(-(1)/(4)*(z)^(2))^(k), k = 0..n - 1)+(- 1)^(n + 1)* ln((1)/(2)*z)*BesselI(n, z)+(- 1)^(n)*(1)/(2)*((1)/(2)*z)^(n)* sum((Psi(k + 1)+ Psi(n + k + 1))*(((1)/(4)*(z)^(2))^(k))/(factorial(k)*factorial(n + k)), k = 0..infinity) |
BesselK[n, z]=Divide[1,2]*(Divide[1,2]*z)^(- n)* Sum[Divide[(n - k - 1)!,(k)!]*(-Divide[1,4]*(z)^(2))^(k), {k, 0, n - 1}]+(- 1)^(n + 1)* Log[Divide[1,2]*z]*BesselI[n, z]+(- 1)^(n)*Divide[1,2]*(Divide[1,2]*z)^(n)* Sum[(PolyGamma[k + 1]+ PolyGamma[n + k + 1])*Divide[(Divide[1,4]*(z)^(2))^(k),(k)!*(n + k)!], {k, 0, Infinity}] |
Error | Failure | - | Successful |
| 10.32.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta}} | BesselI(0, z)=(1)/(Pi)*int(exp(+ z*cos(theta)), theta = 0..Pi) |
BesselI[0, z]=Divide[1,Pi]*Integrate[Exp[+ z*Cos[\[Theta]]], {\[Theta], 0, Pi}] |
Successful | Successful | - | - |
| 10.32.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta}} | BesselI(0, z)=(1)/(Pi)*int(exp(- z*cos(theta)), theta = 0..Pi) |
BesselI[0, z]=Divide[1,Pi]*Integrate[Exp[- z*Cos[\[Theta]]], {\[Theta], 0, Pi}] |
Successful | Successful | - | - |
| 10.32.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}} | (1)/(Pi)*int(exp(+ z*cos(theta)), theta = 0..Pi)=(1)/(Pi)*int(cosh(z*cos(theta)), theta = 0..Pi) |
Divide[1,Pi]*Integrate[Exp[+ z*Cos[\[Theta]]], {\[Theta], 0, Pi}]=Divide[1,Pi]*Integrate[Cosh[z*Cos[\[Theta]]], {\[Theta], 0, Pi}] |
Failure | Failure | Skip | Successful |
| 10.32.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}} | (1)/(Pi)*int(exp(- z*cos(theta)), theta = 0..Pi)=(1)/(Pi)*int(cosh(z*cos(theta)), theta = 0..Pi) |
Divide[1,Pi]*Integrate[Exp[- z*Cos[\[Theta]]], {\[Theta], 0, Pi}]=Divide[1,Pi]*Integrate[Cosh[z*Cos[\[Theta]]], {\[Theta], 0, Pi}] |
Failure | Failure | Skip | Successful |
| 10.32.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}} | BesselI(nu, z)=(((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(+ z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) |
BesselI[\[Nu], z]=Divide[(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[+ z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}] |
Failure | Failure | Skip | Error |
| 10.32.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}} | BesselI(nu, z)=(((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(- z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) |
BesselI[\[Nu], z]=Divide[(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}] |
Failure | Failure | Skip | Error |
| 10.32.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{+ zt}\diff{t}} | (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(+ z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi)=(((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* exp(+ z*t), t = - 1..1) |
Divide[(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[+ z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}]=Divide[(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Exp[+ z*t], {t, - 1, 1}] |
Failure | Failure | Skip | Error |
| 10.32.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{- zt}\diff{t}} | (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(- z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi)=(((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* exp(- z*t), t = - 1..1) |
Divide[(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}]=Divide[(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Exp[- z*t], {t, - 1, 1}] |
Failure | Failure | Skip | Error |
| 10.32.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{n}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{n\theta}\diff{\theta}} | BesselI(n, z)=(1)/(Pi)*int(exp(z*cos(theta))*cos(n*theta), theta = 0..Pi) |
BesselI[n, z]=Divide[1,Pi]*Integrate[Exp[z*Cos[\[Theta]]]*Cos[n*\[Theta]], {\[Theta], 0, Pi}] |
Failure | Failure | Skip | Error |
| 10.32.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-z\cosh@@{t}-\nu t}\diff{t}} | BesselI(nu, z)=(1)/(Pi)*int(exp(z*cos(theta))*cos(nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- z*cosh(t)- nu*t), t = 0..infinity) |
BesselI[\[Nu], z]=Divide[1,Pi]*Integrate[Exp[z*Cos[\[Theta]]]*Cos[\[Nu]*\[Theta]], {\[Theta], 0, Pi}]-Divide[Sin[\[Nu]*Pi],Pi]*Integrate[Exp[- z*Cosh[t]- \[Nu]*t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.32.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}} | BesselK(0, z)= -(1)/(Pi)*int(exp(+ z*cos(theta))*(gamma + ln(2*z*(sin(theta))^(2))), theta = 0..Pi) |
BesselK[0, z]= -Divide[1,Pi]*Integrate[Exp[+ z*Cos[\[Theta]]]*(EulerGamma + Log[2*z*(Sin[\[Theta]])^(2)]), {\[Theta], 0, Pi}] |
Failure | Failure | Skip | Error |
| 10.32.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}} | BesselK(0, z)= -(1)/(Pi)*int(exp(- z*cos(theta))*(gamma + ln(2*z*(sin(theta))^(2))), theta = 0..Pi) |
BesselK[0, z]= -Divide[1,Pi]*Integrate[Exp[- z*Cos[\[Theta]]]*(EulerGamma + Log[2*z*(Sin[\[Theta]])^(2)]), {\[Theta], 0, Pi}] |
Failure | Failure | Skip | Error |
| 10.32.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{0}@{x} = \int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t}} | BesselK(0, x)= int(cos(x*sinh(t)), t = 0..infinity) |
BesselK[0, x]= Integrate[Cos[x*Sinh[t]], {t, 0, Infinity}] |
Successful | Failure | - | Error |
| 10.32.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t} = \int_{0}^{\infty}\frac{\cos@{xt}}{\sqrt{t^{2}+1}}\diff{t}} | int(cos(x*sinh(t)), t = 0..infinity)= int((cos(x*t))/(sqrt((t)^(2)+ 1)), t = 0..infinity) |
Integrate[Cos[x*Sinh[t]], {t, 0, Infinity}]= Integrate[Divide[Cos[x*t],Sqrt[(t)^(2)+ 1]], {t, 0, Infinity}] |
Successful | Failure | - | Error |
| 10.32.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{x} = \sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t}} | BesselK(nu, x)= sec((1)/(2)*nu*Pi)*int(cos(x*sinh(t))*cosh(nu*t), t = 0..infinity) |
BesselK[\[Nu], x]= Sec[Divide[1,2]*\[Nu]*Pi]*Integrate[Cos[x*Sinh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.32.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t} = \csc@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\sin@{x\sinh@@{t}}\sinh@{\nu t}\diff{t}} | sec((1)/(2)*nu*Pi)*int(cos(x*sinh(t))*cosh(nu*t), t = 0..infinity)= csc((1)/(2)*nu*Pi)*int(sin(x*sinh(t))*sinh(nu*t), t = 0..infinity) |
Sec[Divide[1,2]*\[Nu]*Pi]*Integrate[Cos[x*Sinh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}]= Csc[Divide[1,2]*\[Nu]*Pi]*Integrate[Sin[x*Sinh[t]]*Sinh[\[Nu]*t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.32.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t}} | BesselK(nu, z)=((Pi)^((1)/(2))*((1)/(2)*z)^(nu))/(GAMMA(nu +(1)/(2)))*int(exp(- z*cosh(t))*(sinh(t))^(2*nu), t = 0..infinity) |
BesselK[\[Nu], z]=Divide[(Pi)^(Divide[1,2])*(Divide[1,2]*z)^(\[Nu]),Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cosh[t]]*(Sinh[t])^(2*\[Nu]), {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.32.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{1}^{\infty}e^{-zt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}} | ((Pi)^((1)/(2))*((1)/(2)*z)^(nu))/(GAMMA(nu +(1)/(2)))*int(exp(- z*cosh(t))*(sinh(t))^(2*nu), t = 0..infinity)=((Pi)^((1)/(2))*((1)/(2)*z)^(nu))/(GAMMA(nu +(1)/(2)))*int(exp(- z*t)*((t)^(2)- 1)^(nu -(1)/(2)), t = 1..infinity) |
Divide[(Pi)^(Divide[1,2])*(Divide[1,2]*z)^(\[Nu]),Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cosh[t]]*(Sinh[t])^(2*\[Nu]), {t, 0, Infinity}]=Divide[(Pi)^(Divide[1,2])*(Divide[1,2]*z)^(\[Nu]),Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*t]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 10.32.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \int_{0}^{\infty}e^{-z\cosh@@{t}}\cosh@{\nu t}\diff{t}} | BesselK(nu, z)= int(exp(- z*cosh(t))*cosh(nu*t), t = 0..infinity) |
BesselK[\[Nu], z]= Integrate[Exp[- z*Cosh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.32.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \tfrac{1}{2}(\tfrac{1}{2}z)^{\nu}\int_{0}^{\infty}\exp@{-t-\frac{z^{2}}{4t}}\frac{\diff{t}}{t^{\nu+1}}} | BesselK(nu, z)=(1)/(2)*((1)/(2)*z)^(nu)* int(exp(- t -((z)^(2))/(4*t))*(1)/((t)^(nu + 1)), t = 0..infinity) |
BesselK[\[Nu], z]=Divide[1,2]*(Divide[1,2]*z)^(\[Nu])* Integrate[Exp[- t -Divide[(z)^(2),4*t]]*Divide[1,(t)^(\[Nu]+ 1)], {t, 0, Infinity}] |
Successful | Failure | - | Skip |
| 10.32.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{xz} = \frac{\EulerGamma@{\nu+\frac{1}{2}}(2z)^{\nu}}{\pi^{\frac{1}{2}}x^{\nu}}\int_{0}^{\infty}\frac{\cos@{xt}\diff{t}}{(t^{2}+z^{2})^{\nu+\frac{1}{2}}}} | BesselK(nu, x*z)=(GAMMA(nu +(1)/(2))*(2*z)^(nu))/((Pi)^((1)/(2))* (x)^(nu))*int((cos(x*t))/(((t)^(2)+ (z)^(2))^(nu +(1)/(2))), t = 0..infinity) |
BesselK[\[Nu], x*z]=Divide[Gamma[\[Nu]+Divide[1,2]]*(2*z)^(\[Nu]),(Pi)^(Divide[1,2])* (x)^(\[Nu])]*Integrate[Divide[Cos[x*t],((t)^(2)+ (z)^(2))^(\[Nu]+Divide[1,2])], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.32.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty-i\pi}^{\infty+i\pi}e^{z\cosh@@{t}-\nu t}\diff{t}} | BesselI(nu, z)=(1)/(2*Pi*I)*int(exp(z*cosh(t)- nu*t), t = infinity - I*Pi..infinity + I*Pi) |
BesselI[\[Nu], z]=Divide[1,2*Pi*I]*Integrate[Exp[z*Cosh[t]- \[Nu]*t], {t, Infinity - I*Pi, Infinity + I*Pi}] |
Failure | Failure | Skip | Fail
Complex[0.47377882604348887, 0.17987673448701852] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.5712028891376235, 2.011728577446344] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.630703522037926, 7.3730343474306625] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.4462596814449855, 3.2604536086998377] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.32.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{4\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(\tfrac{1}{2}z)^{-2t}\diff{t}} | BesselK(nu, z)=(((1)/(2)*z)^(nu))/(4*Pi*I)*int(GAMMA(t)*GAMMA(t - nu)*((1)/(2)*z)^(- 2*t), t = c - I*infinity..c + I*infinity) |
BesselK[\[Nu], z]=Divide[(Divide[1,2]*z)^(\[Nu]),4*Pi*I]*Integrate[Gamma[t]*Gamma[t - \[Nu]]*(Divide[1,2]*z)^(- 2*t), {t, c - I*Infinity, c + I*Infinity}] |
Failure | Failure | Skip | Error |
| 10.32.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \frac{1}{2\pi^{2}i}\left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\cos@{\nu\pi}\*\int_{-i\infty}^{i\infty}\EulerGamma@{t}\EulerGamma@{\tfrac{1}{2}-t-\nu}\EulerGamma@{\tfrac{1}{2}-t+\nu}(2z)^{t}\diff{t}} | BesselK(nu, z)=(1)/(2*(Pi)^(2)* I)*((Pi)/(2*z))^((1)/(2))* exp(- z)*cos(nu*Pi)* int(GAMMA(t)*GAMMA((1)/(2)- t - nu)*GAMMA((1)/(2)- t + nu)*(2*z)^(t), t = - I*infinity..I*infinity) |
BesselK[\[Nu], z]=Divide[1,2*(Pi)^(2)* I]*(Divide[Pi,2*z])^(Divide[1,2])* Exp[- z]*Cos[\[Nu]*Pi]* Integrate[Gamma[t]*Gamma[Divide[1,2]- t - \[Nu]]*Gamma[Divide[1,2]- t + \[Nu]]*(2*z)^(t), {t, - I*Infinity, I*Infinity}] |
Failure | Failure | Skip | Error |
| 10.32.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\mu}@{z}\modBesselI{\nu}@{z} = \frac{2}{\pi}\int_{0}^{\frac{1}{2}\pi}\modBesselI{\mu+\nu}@{2z\cos@@{\theta}}\cos@{(\mu-\nu)\theta}\diff{\theta}} | BesselI(mu, z)*BesselI(nu, z)=(2)/(Pi)*int(BesselI(mu + nu, 2*z*cos(theta))*cos((mu - nu)* theta), theta = 0..(1)/(2)*Pi) |
BesselI[\[Mu], z]*BesselI[\[Nu], z]=Divide[2,Pi]*Integrate[BesselI[\[Mu]+ \[Nu], 2*z*Cos[\[Theta]]]*Cos[(\[Mu]- \[Nu])* \[Theta]], {\[Theta], 0, Divide[1,2]*Pi}] |
Failure | Failure | Skip | Skip |
| 10.32.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu+\nu}@{2x\sinh@@{t}}e^{(-\mu+\nu)t}\diff{t}} | BesselI(mu, x)*BesselK(nu, x)= int(BesselJ(mu + nu, 2*x*sinh(t))*exp((- mu + nu)* t), t = 0..infinity) |
BesselI[\[Mu], x]*BesselK[\[Nu], x]= Integrate[BesselJ[\[Mu]+ \[Nu], 2*x*Sinh[t]]*Exp[(- \[Mu]+ \[Nu])* t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.32.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu-\nu}@{2x\sinh@@{t}}e^{(-\mu-\nu)t}\diff{t}} | BesselI(mu, x)*BesselK(nu, x)= int(BesselJ(mu - nu, 2*x*sinh(t))*exp((- mu - nu)* t), t = 0..infinity) |
BesselI[\[Mu], x]*BesselK[\[Nu], x]= Integrate[BesselJ[\[Mu]- \[Nu], 2*x*Sinh[t]]*Exp[(- \[Mu]- \[Nu])* t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.32.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu+\nu}@{2z\cosh@@{t}}\cosh@{(\mu-\nu)t}\diff{t}} | BesselK(mu, z)*BesselK(nu, z)= 2*int(BesselK(mu + nu, 2*z*cosh(t))*cosh((mu - nu)* t), t = 0..infinity) |
BesselK[\[Mu], z]*BesselK[\[Nu], z]= 2*Integrate[BesselK[\[Mu]+ \[Nu], 2*z*Cosh[t]]*Cosh[(\[Mu]- \[Nu])* t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.32.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu-\nu}@{2z\cosh@@{t}}\cosh@{(\mu+\nu)t}\diff{t}} | BesselK(mu, z)*BesselK(nu, z)= 2*int(BesselK(mu - nu, 2*z*cosh(t))*cosh((mu + nu)* t), t = 0..infinity) |
BesselK[\[Mu], z]*BesselK[\[Nu], z]= 2*Integrate[BesselK[\[Mu]- \[Nu], 2*z*Cosh[t]]*Cosh[(\[Mu]+ \[Nu])* t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 10.32.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z}\modBesselK{\nu}@{\zeta} = \frac{1}{2}\int_{0}^{\infty}\exp@{-\frac{t}{2}-\frac{z^{2}+\zeta^{2}}{2t}}\modBesselK{\nu}\left(\frac{z\zeta}{t}\right)\frac{\diff{t}}{t}} | BesselK(nu, z)*BesselK(nu, zeta)=(1)/(2)*int(exp(-(t)/(2)-((z)^(2)+ (zeta)^(2))/(2*t))*BesselK(nu, ((z*zeta)/(t))*)*(1)/(t), t = 0..infinity) |
BesselK[\[Nu], z]*BesselK[\[Nu], \[zeta]]=Divide[1,2]*Integrate[Exp[-Divide[t,2]-Divide[(z)^(2)+ (\[zeta])^(2),2*t]]*BesselK[\[Nu], (Divide[z*\[zeta],t])*]*Divide[1,t], {t, 0, Infinity}] |
Error | Failure | - | Error |
| 10.32.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = \frac{1}{8\pi i}\int_{c-i\infty}^{c+i\infty}\frac{\EulerGamma@{t+\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t+\frac{1}{2}\mu-\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu-\frac{1}{2}\nu}}{\EulerGamma@{2t}}(\tfrac{1}{2}z)^{-2t}\diff{t}} | BesselK(mu, z)*BesselK(nu, z)=(1)/(8*Pi*I)*int((GAMMA(t +(1)/(2)*mu +(1)/(2)*nu)*GAMMA(t +(1)/(2)*mu -(1)/(2)*nu)*GAMMA(t -(1)/(2)*mu +(1)/(2)*nu)*GAMMA(t -(1)/(2)*mu -(1)/(2)*nu))/(GAMMA(2*t))*((1)/(2)*z)^(- 2*t), t = c - I*infinity..c + I*infinity) |
BesselK[\[Mu], z]*BesselK[\[Nu], z]=Divide[1,8*Pi*I]*Integrate[Divide[Gamma[t +Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]]*Gamma[t +Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]]*Gamma[t -Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]]*Gamma[t -Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]],Gamma[2*t]]*(Divide[1,2]*z)^(- 2*t), {t, c - I*Infinity, c + I*Infinity}] |
Failure | Failure | Skip | Error |
| 10.34.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{ze^{m\pi i}} = e^{m\nu\pi i}\modBesselI{\nu}@{z}} | BesselI(nu, z*exp(m*Pi*I))= exp(m*nu*Pi*I)*BesselI(nu, z) |
BesselI[\[Nu], z*Exp[m*Pi*I]]= Exp[m*\[Nu]*Pi*I]*BesselI[\[Nu], z] |
Failure | Failure | Fail -25.46648651+34.76058054*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}.4738478497+.1798644481*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}-25.46593127+34.75464498*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}-2.571651015-2.011784848*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}... skip entries to safe data |
Fail
Complex[-25.466486497459893, 34.76058068352855] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.47384785056443346, 0.17986444785635414] <- {Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-25.465931246406512, 34.754645199849094] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-223.08150600961898, -165.2079311070147] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.34.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{ze^{m\pi i}} = e^{-m\nu\pi i}\modBesselK{\nu}@{z}-\pi i\sin@{m\nu\pi}\csc@{\nu\pi}\modBesselI{\nu}@{z}} | BesselK(nu, z*exp(m*Pi*I))= exp(- m*nu*Pi*I)*BesselK(nu, z)- Pi*I*sin(m*nu*Pi)*csc(nu*Pi)*BesselI(nu, z) |
BesselK[\[Nu], z*Exp[m*Pi*I]]= Exp[- m*\[Nu]*Pi*I]*BesselK[\[Nu], z]- Pi*I*Sin[m*\[Nu]*Pi]*Csc[\[Nu]*Pi]*BesselI[\[Nu], z] |
Failure | Failure | Fail -23.72816996-16.20095675*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}1974.016674-1497.794581*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}78036.43688+195659.8555*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}-346.8741250+807.6398259*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}... skip entries to safe data |
Fail
Complex[-23.728169968169517, -16.200956740051907] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1974.0166738862135, -1497.7945856695665] <- {Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[78036.4381344157, 195659.85598804062] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-16.563048824383813, -6.675705970582722] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.34.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{ze^{m\pi i}} = (i/\pi)\left(+ e^{m\nu\pi i}\modBesselK{\nu}@{ze^{+\pi i}}- e^{(m- 1)\nu\pi i}\modBesselK{\nu}@{z}\right)} | BesselI(nu, z*exp(m*Pi*I))=(I/ Pi)*(+ exp(m*nu*Pi*I)*BesselK(nu, z*exp(+ Pi*I))- exp((m - 1)* nu*Pi*I)*BesselK(nu, z)) |
BesselI[\[Nu], z*Exp[m*Pi*I]]=(I/ Pi)*(+ Exp[m*\[Nu]*Pi*I]*BesselK[\[Nu], z*Exp[+ Pi*I]]- Exp[(m - 1)* \[Nu]*Pi*I]*BesselK[\[Nu], z]) |
Failure | Failure | Fail -25.36470622+34.79539330*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}.4739237916+.1786015012*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}-25.46594582+34.75464807*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}-2.571651015-2.011784848*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}... skip entries to safe data |
Fail
Complex[-25.36470621174673, 34.79539343891294] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.47392379247751504, 0.17860150099441258] <- {Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-25.465945802770374, 34.75464829402328] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[257.07974135711925, -110.41346285737623] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.34.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{ze^{m\pi i}} = (i/\pi)\left(- e^{m\nu\pi i}\modBesselK{\nu}@{ze^{-\pi i}}+ e^{(m+ 1)\nu\pi i}\modBesselK{\nu}@{z}\right)} | BesselI(nu, z*exp(m*Pi*I))=(I/ Pi)*(- exp(m*nu*Pi*I)*BesselK(nu, z*exp(- Pi*I))+ exp((m + 1)* nu*Pi*I)*BesselK(nu, z)) |
BesselI[\[Nu], z*Exp[m*Pi*I]]=(I/ Pi)*(- Exp[m*\[Nu]*Pi*I]*BesselK[\[Nu], z*Exp[- Pi*I]]+ Exp[(m + 1)* \[Nu]*Pi*I]*BesselK[\[Nu], z]) |
Failure | Failure | Fail -25.46648651+34.76058054*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}.4738478497+.1798644481*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}-25.46593127+34.75464498*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}-.5311818950e-1+.4060217813e-1*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 1}... skip entries to safe data |
Fail
Complex[-25.466486497459893, 34.76058068352855] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.47384785056443346, 0.17986444785635414] <- {Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-25.465931246406512, 34.754645199849094] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-223.0815060096189, -165.20793110701467] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.34.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{ze^{m\pi i}} = \csc@{\nu\pi}\left(+\sin@{m\nu\pi}\modBesselK{\nu}@{ze^{+\pi i}}-\sin@{(m- 1)\nu\pi}\modBesselK{\nu}@{z}\right)} | BesselK(nu, z*exp(m*Pi*I))= csc(nu*Pi)*(+ sin(m*nu*Pi)*BesselK(nu, z*exp(+ Pi*I))- sin((m - 1)* nu*Pi)*BesselK(nu, z)) |
BesselK[\[Nu], z*Exp[m*Pi*I]]= Csc[\[Nu]*Pi]*(+ Sin[m*\[Nu]*Pi]*BesselK[\[Nu], z*Exp[+ Pi*I]]- Sin[(m - 1)* \[Nu]*Pi]*BesselK[\[Nu], z]) |
Failure | Failure | Fail 109.3129522+79.68557470*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}-9027.967286+7136.744811*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}-346.8741247+807.6398251*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}-58340.79702-46700.99889*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 3}... skip entries to safe data |
Fail
Complex[109.31295240645538, 79.68557469528692] <- {Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-9027.967291383398, 7136.744876012727] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-346.8741237701426, -807.6398268342901] <- {Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-58340.79750295953, 46700.99881352048] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.34.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{ze^{m\pi i}} = \csc@{\nu\pi}\left(-\sin@{m\nu\pi}\modBesselK{\nu}@{ze^{-\pi i}}+\sin@{(m+ 1)\nu\pi}\modBesselK{\nu}@{z}\right)} | BesselK(nu, z*exp(m*Pi*I))= csc(nu*Pi)*(- sin(m*nu*Pi)*BesselK(nu, z*exp(- Pi*I))+ sin((m + 1)* nu*Pi)*BesselK(nu, z)) |
BesselK[\[Nu], z*Exp[m*Pi*I]]= Csc[\[Nu]*Pi]*(- Sin[m*\[Nu]*Pi]*BesselK[\[Nu], z*Exp[- Pi*I]]+ Sin[(m + 1)* \[Nu]*Pi]*BesselK[\[Nu], z]) |
Failure | Failure | Fail -23.72816993-16.20095676*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}1974.016672-1497.794570*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}78036.44012+195659.8571*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}-16.56304884+6.675705955*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 1}... skip entries to safe data |
Fail
Complex[-23.728169968169517, -16.2009567400519] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1974.0166738862144, -1497.7945856695726] <- {Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[78036.43813441524, 195659.85598804036] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-16.563048824383813, -6.675705970582721] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.34.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{n}@{ze^{m\pi i}} = (-1)^{mn}\modBesselK{n}@{z}+(-1)^{n(m-1)-1}m\pi i\modBesselI{n}@{z}} | BesselK(n, z*exp(m*Pi*I))=(- 1)^(m*n)* BesselK(n, z)+(- 1)^(n*(m - 1)- 1)* m*Pi*I*BesselI(n, z) |
BesselK[n, z*Exp[m*Pi*I]]=(- 1)^(m*n)* BesselK[n, z]+(- 1)^(n*(m - 1)- 1)* m*Pi*I*BesselI[n, z] |
Failure | Failure | Fail -6.264823649+1.883544620*I <- {z = 2^(1/2)+I*2^(1/2), m = 1, n = 1}-3.011056351-1.038481291*I <- {z = 2^(1/2)+I*2^(1/2), m = 1, n = 2}-.5379125927-.9060977874*I <- {z = 2^(1/2)+I*2^(1/2), m = 1, n = 3}6.264823651-1.883544623*I <- {z = 2^(1/2)+I*2^(1/2), m = 2, n = 1}... skip entries to safe data |
Fail
Complex[-6.264823652701258, 1.8835446212245166] <- {Rule[m, 1], Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.0110563535593116, -1.0384812903661844] <- {Rule[m, 1], Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.537912595321433, -0.9060977859421694] <- {Rule[m, 1], Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.264823652701258, -1.8835446212245166] <- {Rule[m, 2], Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.34.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{n}@{ze^{m\pi i}} = +(-1)^{n(m-1)}m\modBesselK{n}@{ze^{+\pi i}}-(-1)^{nm}(m- 1)\modBesselK{n}@{z}} | BesselK(n, z*exp(m*Pi*I))= +(- 1)^(n*(m - 1))* m*BesselK(n, z*exp(+ Pi*I))-(- 1)^(n*m)*(m - 1)* BesselK(n, z) |
BesselK[n, z*Exp[m*Pi*I]]= +(- 1)^(n*(m - 1))* m*BesselK[n, z*Exp[+ Pi*I]]-(- 1)^(n*m)*(m - 1)* BesselK[n, z] |
Failure | Failure | Fail -6.264823650+1.883544622*I <- {z = 2^(1/2)+I*2^(1/2), m = 2, n = 1}3.011056351+1.038481289*I <- {z = 2^(1/2)+I*2^(1/2), m = 2, n = 2}-.5379125964-.9060977833*I <- {z = 2^(1/2)+I*2^(1/2), m = 2, n = 3}6.264823652-1.883544629*I <- {z = 2^(1/2)+I*2^(1/2), m = 3, n = 1}... skip entries to safe data |
Fail
Complex[-6.264823652701258, 1.8835446212245168] <- {Rule[m, 2], Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.0110563535593116, 1.0384812903661842] <- {Rule[m, 2], Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.537912595321433, -0.9060977859421694] <- {Rule[m, 2], Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.264823652701258, -1.8835446212245168] <- {Rule[m, 3], Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.34.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{n}@{ze^{m\pi i}} = -(-1)^{n(m-1)}m\modBesselK{n}@{ze^{-\pi i}}+(-1)^{nm}(m+ 1)\modBesselK{n}@{z}} | BesselK(n, z*exp(m*Pi*I))= -(- 1)^(n*(m - 1))* m*BesselK(n, z*exp(- Pi*I))+(- 1)^(n*m)*(m + 1)* BesselK(n, z) |
BesselK[n, z*Exp[m*Pi*I]]= -(- 1)^(n*(m - 1))* m*BesselK[n, z*Exp[- Pi*I]]+(- 1)^(n*m)*(m + 1)* BesselK[n, z] |
Failure | Failure | Fail -6.264823648+1.883544620*I <- {z = 2^(1/2)+I*2^(1/2), m = 1, n = 1}-3.011056351-1.038481291*I <- {z = 2^(1/2)+I*2^(1/2), m = 1, n = 2}-.537912592-.9060977875*I <- {z = 2^(1/2)+I*2^(1/2), m = 1, n = 3}6.264823649-1.883544623*I <- {z = 2^(1/2)+I*2^(1/2), m = 2, n = 1}... skip entries to safe data |
Fail
Complex[-6.264823652701258, 1.8835446212245168] <- {Rule[m, 1], Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.0110563535593116, -1.0384812903661842] <- {Rule[m, 1], Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.537912595321433, -0.9060977859421694] <- {Rule[m, 1], Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.264823652701258, -1.8835446212245168] <- {Rule[m, 2], Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.34#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{\conj{z}} = \conj{\modBesselI{\nu}@{z}}} | BesselI(nu, conjugate(z))= conjugate(BesselI(nu, z)) |
BesselI[\[Nu], Conjugate[z]]= Conjugate[BesselI[\[Nu], z]] |
Failure | Failure | Fail -3.044981713-1.831851844*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}3.044981713-1.831851844*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}25.45117532+34.79009675*I <- {nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-25.45117532+34.79009675*I <- {nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-3.0449817151811125, -1.8318518429593253] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.0449817151811125, 1.8318518429593253] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[6.0769632034829115, 4.112580738730825] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-6.0769632034829115, -4.112580738730825] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.34#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{\conj{z}} = \conj{\modBesselK{\nu}@{z}}} | BesselK(nu, conjugate(z))= conjugate(BesselK(nu, z)) |
BesselK[\[Nu], Conjugate[z]]= Conjugate[BesselK[\[Nu], z]] |
Failure | Failure | Fail -.2418444739-.2420650681*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}.2418444739-.2420650681*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-9.672734607+.86628375e-1*I <- {nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}9.672734607+.86628375e-1*I <- {nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-0.2418444736872933, -0.24206506816430606] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.2418444736872933, 0.24206506816430606] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.2418444736872933, -0.24206506816430606] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.2418444736872933, 0.24206506816430606] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.35.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{\frac{1}{2}z(t+t^{-1})} = \sum_{m=-\infty}^{\infty}t^{m}\modBesselI{m}@{z}} | exp((1)/(2)*z*(t + (t)^(- 1)))= sum((t)^(m)* BesselI(m, z), m = - infinity..infinity) |
Exp[Divide[1,2]*z*(t + (t)^(- 1))]= Sum[(t)^(m)* BesselI[m, z], {m, - Infinity, Infinity}] |
Failure | Failure | Skip | Error |
| 10.35.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{z\cos@@{\theta}} = \modBesselI{0}@{z}+2\sum_{k=1}^{\infty}\modBesselI{k}@{z}\cos@{k\theta}} | exp(z*cos(theta))= BesselI(0, z)+ 2*sum(BesselI(k, z)*cos(k*theta), k = 1..infinity) |
Exp[z*Cos[\[Theta]]]= BesselI[0, z]+ 2*Sum[BesselI[k, z]*Cos[k*\[Theta]], {k, 1, Infinity}] |
Failure | Successful | Skip | - |
| 10.35.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{z\sin@@{\theta}} = \modBesselI{0}@{z}+2\sum_{k=0}^{\infty}(-1)^{k}\modBesselI{2k+1}@{z}\sin@{(2k+1)\theta}+2\sum_{k=1}^{\infty}(-1)^{k}\modBesselI{2k}@{z}\cos@{2k\theta}} | exp(z*sin(theta))= BesselI(0, z)+ 2*sum((- 1)^(k)* BesselI(2*k + 1, z)*sin((2*k + 1)* theta), k = 0..infinity)+ 2*sum((- 1)^(k)* BesselI(2*k, z)*cos(2*k*theta), k = 1..infinity) |
Exp[z*Sin[\[Theta]]]= BesselI[0, z]+ 2*Sum[(- 1)^(k)* BesselI[2*k + 1, z]*Sin[(2*k + 1)* \[Theta]], {k, 0, Infinity}]+ 2*Sum[(- 1)^(k)* BesselI[2*k, z]*Cos[2*k*\[Theta]], {k, 1, Infinity}] |
Failure | Failure | Skip | Skip |
| 10.37.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\modBesselK{\nu}@{z}| < |\modBesselK{\mu}@{z}|} | abs(BesselK(nu, z))<abs(BesselK(mu, z)) |
Abs[BesselK[\[Nu], z]]<Abs[BesselK[\[Mu], z]] |
Failure | Failure | Fail .3485691514 < .3485691514 <- {mu = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}.1206554296 < .1206554296 <- {mu = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}1.592895962 < 1.592895962 <- {mu = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}10.33727274 < 10.33727274 <- {mu = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Successful |
| 10.38.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\modBesselI{+\nu}@{z}}{\nu} = +\modBesselI{+\nu}@{z}\ln@{\tfrac{1}{2}z}-(\tfrac{1}{2}z)^{+\nu}\sum_{k=0}^{\infty}\frac{\digamma@{k+1+\nu}}{\EulerGamma@{k+1+\nu}}\frac{(\frac{1}{4}z^{2})^{k}}{k!}} | diff(BesselI(+ nu, z), nu)= + BesselI(+ nu, z)*ln((1)/(2)*z)-((1)/(2)*z)^(+ nu)* sum((Psi(k + 1 + nu))/(GAMMA(k + 1 + nu))*(((1)/(4)*(z)^(2))^(k))/(factorial(k)), k = 0..infinity) |
D[BesselI[+ \[Nu], z], \[Nu]]= + BesselI[+ \[Nu], z]*Log[Divide[1,2]*z]-(Divide[1,2]*z)^(+ \[Nu])* Sum[Divide[PolyGamma[k + 1 + \[Nu]],Gamma[k + 1 + \[Nu]]]*Divide[(Divide[1,4]*(z)^(2))^(k),(k)!], {k, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 10.38.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\modBesselI{-\nu}@{z}}{\nu} = -\modBesselI{-\nu}@{z}\ln@{\tfrac{1}{2}z}+(\tfrac{1}{2}z)^{-\nu}\sum_{k=0}^{\infty}\frac{\digamma@{k+1-\nu}}{\EulerGamma@{k+1-\nu}}\frac{(\frac{1}{4}z^{2})^{k}}{k!}} | diff(BesselI(- nu, z), nu)= - BesselI(- nu, z)*ln((1)/(2)*z)+((1)/(2)*z)^(- nu)* sum((Psi(k + 1 - nu))/(GAMMA(k + 1 - nu))*(((1)/(4)*(z)^(2))^(k))/(factorial(k)), k = 0..infinity) |
D[BesselI[- \[Nu], z], \[Nu]]= - BesselI[- \[Nu], z]*Log[Divide[1,2]*z]+(Divide[1,2]*z)^(- \[Nu])* Sum[Divide[PolyGamma[k + 1 - \[Nu]],Gamma[k + 1 - \[Nu]]]*Divide[(Divide[1,4]*(z)^(2))^(k),(k)!], {k, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 10.38.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\modBesselK{\nu}@{z}}{\nu} = \tfrac{1}{2}\pi\csc@{\nu\pi}\*\left(\pderiv{\modBesselI{-\nu}@{z}}{\nu}-\pderiv{\modBesselI{\nu}@{z}}{\nu}\right)-\pi\cot@{\nu\pi}\modBesselK{\nu}@{z}} | diff(BesselK(nu, z), nu)=(1)/(2)*Pi*csc(nu*Pi)*(diff(BesselI(- nu, z), nu)- diff(BesselI(nu, z), nu))- Pi*cot(nu*Pi)*BesselK(nu, z) |
D[BesselK[\[Nu], z], \[Nu]]=Divide[1,2]*Pi*Csc[\[Nu]*Pi]*(D[BesselI[- \[Nu], z], \[Nu]]- D[BesselI[\[Nu], z], \[Nu]])- Pi*Cot[\[Nu]*Pi]*BesselK[\[Nu], z] |
Successful | Failure | - | Successful |
| 10.39#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sinh@@{z}} | BesselI((1)/(2), z)=((2)/(Pi*z))^((1)/(2))* sinh(z) |
BesselI[Divide[1,2], z]=(Divide[2,Pi*z])^(Divide[1,2])* Sinh[z] |
Failure | Failure | Successful | Successful |
| 10.39#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{-\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\cosh@@{z}} | BesselI(-(1)/(2), z)=((2)/(Pi*z))^((1)/(2))* cosh(z) |
BesselI[-Divide[1,2], z]=(Divide[2,Pi*z])^(Divide[1,2])* Cosh[z] |
Failure | Failure | Successful | Successful |
| 10.39.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\frac{1}{2}}@{z} = \modBesselK{-\frac{1}{2}}@{z}} | BesselK((1)/(2), z)= BesselK(-(1)/(2), z) |
BesselK[Divide[1,2], z]= BesselK[-Divide[1,2], z] |
Successful | Successful | - | - |
| 10.39.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{-\frac{1}{2}}@{z} = \left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}} | BesselK(-(1)/(2), z)=((Pi)/(2*z))^((1)/(2))* exp(- z) |
BesselK[-Divide[1,2], z]=(Divide[Pi,2*z])^(Divide[1,2])* Exp[- z] |
Failure | Failure | Successful | Successful |
| 10.39.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\frac{1}{4}}@{z} = \pi^{\frac{1}{2}}z^{-\frac{1}{4}}\paraU@{0}{2z^{\frac{1}{2}}}} | BesselK((1)/(4), z)= (Pi)^((1)/(2))* (z)^(-(1)/(4))* CylinderU(0, 2*(z)^((1)/(2))) |
BesselK[Divide[1,4], z]= (Pi)^(Divide[1,2])* (z)^(-Divide[1,4])* ParabolicCylinderD[-0 - 1/2, 2*(z)^(Divide[1,2])] |
Successful | Failure | - | Successful |
| 10.39.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\frac{3}{4}}@{z} = \tfrac{1}{2}\pi^{\frac{1}{2}}z^{-\frac{3}{4}}\left(\tfrac{1}{2}\paraU@{1}{2z^{\frac{1}{2}}}+\paraU@{-1}{2z^{\frac{1}{2}}}\right)} | BesselK((3)/(4), z)=(1)/(2)*(Pi)^((1)/(2))* (z)^(-(3)/(4))*((1)/(2)*CylinderU(1, 2*(z)^((1)/(2)))+ CylinderU(- 1, 2*(z)^((1)/(2)))) |
BesselK[Divide[3,4], z]=Divide[1,2]*(Pi)^(Divide[1,2])* (z)^(-Divide[3,4])*(Divide[1,2]*ParabolicCylinderD[-1 - 1/2, 2*(z)^(Divide[1,2])]+ ParabolicCylinderD[-- 1 - 1/2, 2*(z)^(Divide[1,2])]) |
Failure | Failure | Successful | Fail
Complex[-0.24654129480515125, -0.14875200582767972] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[PreDecrement[1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.5994174244432623, -0.2209182787401364] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[PreDecrement[1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.045375099662282176, -0.23186773164961136] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[PreDecrement[1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.05931481647092712, -0.20328323070426188] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[PreDecrement[1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.39.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}e^{+ z}}{\EulerGamma@{\nu+1}}\KummerconfhyperM@{\nu+\tfrac{1}{2}}{2\nu+1}{- 2z}} | BesselI(nu, z)=(((1)/(2)*z)^(nu)* exp(+ z))/(GAMMA(nu + 1))*KummerM(nu +(1)/(2), 2*nu + 1, - 2*z) |
BesselI[\[Nu], z]=Divide[(Divide[1,2]*z)^(\[Nu])* Exp[+ z],Gamma[\[Nu]+ 1]]*Hypergeometric1F1[\[Nu]+Divide[1,2], 2*\[Nu]+ 1, - 2*z] |
Failure | Successful | Successful | - |
| 10.39.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}e^{- z}}{\EulerGamma@{\nu+1}}\KummerconfhyperM@{\nu+\tfrac{1}{2}}{2\nu+1}{+ 2z}} | BesselI(nu, z)=(((1)/(2)*z)^(nu)* exp(- z))/(GAMMA(nu + 1))*KummerM(nu +(1)/(2), 2*nu + 1, + 2*z) |
BesselI[\[Nu], z]=Divide[(Divide[1,2]*z)^(\[Nu])* Exp[- z],Gamma[\[Nu]+ 1]]*Hypergeometric1F1[\[Nu]+Divide[1,2], 2*\[Nu]+ 1, + 2*z] |
Successful | Successful | - | - |
| 10.39.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \pi^{\frac{1}{2}}(2z)^{\nu}e^{-z}\KummerconfhyperU@{\nu+\tfrac{1}{2}}{2\nu+1}{2z}} | BesselK(nu, z)= (Pi)^((1)/(2))*(2*z)^(nu)* exp(- z)*KummerU(nu +(1)/(2), 2*nu + 1, 2*z) |
BesselK[\[Nu], z]= (Pi)^(Divide[1,2])*(2*z)^(\[Nu])* Exp[- z]*HypergeometricU[\[Nu]+Divide[1,2], 2*\[Nu]+ 1, 2*z] |
Successful | Successful | - | - |
| 10.39.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(2z)^{-\frac{1}{2}}\WhittakerconfhyperM{0}{\nu}@{2z}}{2^{2\nu}\EulerGamma@{\nu+1}}} | BesselI(nu, z)=((2*z)^(-(1)/(2))* WhittakerM(0, nu, 2*z))/((2)^(2*nu)* GAMMA(nu + 1)) |
BesselI[\[Nu], z]=Divide[(2*z)^(-Divide[1,2])* WhittakerM[0, \[Nu], 2*z],(2)^(2*\[Nu])* Gamma[\[Nu]+ 1]] |
Successful | Successful | - | - |
| 10.39.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \left(\frac{\pi}{2z}\right)^{\frac{1}{2}}\WhittakerconfhyperW{0}{\nu}@{2z}} | BesselK(nu, z)=((Pi)/(2*z))^((1)/(2))* WhittakerW(0, nu, 2*z) |
BesselK[\[Nu], z]=(Divide[Pi,2*z])^(Divide[1,2])* WhittakerW[0, \[Nu], 2*z] |
Failure | Failure | Successful | Successful |
| 10.39.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+1}}\genhyperF{0}{1}@{-}{\nu+1}{\tfrac{1}{4}z^{2}}} | BesselI(nu, z)=(((1)/(2)*z)^(nu))/(GAMMA(nu + 1))*hypergeom([-], [nu + 1], (1)/(4)*(z)^(2)) |
BesselI[\[Nu], z]=Divide[(Divide[1,2]*z)^(\[Nu]),Gamma[\[Nu]+ 1]]*HypergeometricPFQ[{-}, {\[Nu]+ 1}, Divide[1,4]*(z)^(2)] |
Error | Failure | - | Error |
| 10.40.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\left(\sum_{k=0}^{\ell-1}\frac{a_{k}(\nu)}{z^{k}}+R_{\ell}(\nu,z)\right)} | BesselK(nu, z)=((Pi)/(2*z))^((1)/(2))* exp(- z)*(sum((a[k]*(nu))/((z)^(k)), k = 0..ell - 1)+ R[ell]*(nu , z)) |
BesselK[\[Nu], z]=(Divide[Pi,2*z])^(Divide[1,2])* Exp[- z]*(Sum[Divide[Subscript[a, k]*(\[Nu]),(z)^(k)], {k, 0, \[ScriptL]- 1}]+ Subscript[R, \[ScriptL]]*(\[Nu], z)) |
Failure | Failure | Skip | Error |
| 10.40.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{\ell}(\nu,z) = (-1)^{\ell}2\cos@{\nu\pi}\*\left(\sum_{k=0}^{m-1}\frac{a_{k}(\nu)}{z^{k}}\scterminant{\ell-k}@{2z}+R_{m,\ell}(\nu,z)\right)} | R[ell]*(nu , z)=(- 1)^(ell)* 2*cos(nu*Pi)*(sum((a[k]*(nu))/((z)^(k))*(exp(2*z)/(2*Pi))*GAMMA(ell - k)*GAMMA(1-ell - k,2*z), k = 0..m - 1)+ R[m , ell]*(nu , z)) |
Error |
Failure | Error | Skip | - |
| 10.43.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\frac{\modBesselI{0}@{t}-1}{t}\diff{t} = \frac{1}{2}\sum_{k=1}^{\infty}(-1)^{k-1}\frac{\digamma@{k+1}-\digamma@{1}}{k!}(\tfrac{1}{2}x)^{k}\modBesselI{k}@{x}} | int((BesselI(0, t)- 1)/(t), t = 0..x)=(1)/(2)*sum((- 1)^(k - 1)*(Psi(k + 1)- Psi(1))/(factorial(k))*((1)/(2)*x)^(k)* BesselI(k, x), k = 1..infinity) |
Integrate[Divide[BesselI[0, t]- 1,t], {t, 0, x}]=Divide[1,2]*Sum[(- 1)^(k - 1)*Divide[PolyGamma[k + 1]- PolyGamma[1],(k)!]*(Divide[1,2]*x)^(k)* BesselI[k, x], {k, 1, Infinity}] |
Failure | Failure | Skip | Skip |
| 10.43.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2}\sum_{k=1}^{\infty}(-1)^{k-1}\frac{\digamma@{k+1}-\digamma@{1}}{k!}(\tfrac{1}{2}x)^{k}\modBesselI{k}@{x} = \frac{2}{x}\sum_{k=0}^{\infty}(-1)^{k}(2k+3)(\digamma@{k+2}-\digamma@{1})\modBesselI{2k+3}@{x}} | (1)/(2)*sum((- 1)^(k - 1)*(Psi(k + 1)- Psi(1))/(factorial(k))*((1)/(2)*x)^(k)* BesselI(k, x), k = 1..infinity)=(2)/(x)*sum((- 1)^(k)*(2*k + 3)*(Psi(k + 2)- Psi(1))* BesselI(2*k + 3, x), k = 0..infinity) |
Divide[1,2]*Sum[(- 1)^(k - 1)*Divide[PolyGamma[k + 1]- PolyGamma[1],(k)!]*(Divide[1,2]*x)^(k)* BesselI[k, x], {k, 1, Infinity}]=Divide[2,x]*Sum[(- 1)^(k)*(2*k + 3)*(PolyGamma[k + 2]- PolyGamma[1])* BesselI[2*k + 3, x], {k, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 10.43.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}\frac{\modBesselK{0}@{t}}{t}\diff{t} = \frac{1}{2}\left(\ln@{\tfrac{1}{2}x}+\EulerConstant\right)^{2}+\frac{\pi^{2}}{24}-\sum_{k=1}^{\infty}\left(\digamma@{k+1}+\frac{1}{2k}-\ln@{\tfrac{1}{2}x}\right)\frac{(\tfrac{1}{2}x)^{2k}}{2k(k!)^{2}}} | int((BesselK(0, t))/(t), t = x..infinity)=(1)/(2)*(ln((1)/(2)*x)+ gamma)^(2)+((Pi)^(2))/(24)- sum((Psi(k + 1)+(1)/(2*k)- ln((1)/(2)*x))*(((1)/(2)*x)^(2*k))/(2*k*(factorial(k))^(2)), k = 1..infinity) |
Integrate[Divide[BesselK[0, t],t], {t, x, Infinity}]=Divide[1,2]*(Log[Divide[1,2]*x]+ EulerGamma)^(2)+Divide[(Pi)^(2),24]- Sum[(PolyGamma[k + 1]+Divide[1,2*k]- Log[Divide[1,2]*x])*Divide[(Divide[1,2]*x)^(2*k),2*k*((k)!)^(2)], {k, 1, Infinity}] |
Failure | Failure | Skip | Skip |
| 10.43.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{-t}\modBesselI{n}@{t}\diff{t} = xe^{-x}(\modBesselI{0}@{x}+\modBesselI{1}@{x})+n(e^{-x}\modBesselI{0}@{x}-1)+2e^{-x}\sum_{k=1}^{n-1}(n-k)\modBesselI{k}@{x}} | int(exp(- t)*BesselI(n, t), t = 0..x)= x*exp(- x)*(BesselI(0, x)+ BesselI(1, x))+ n*(exp(- x)*BesselI(0, x)- 1)+ 2*exp(- x)*sum((n - k)* BesselI(k, x), k = 1..n - 1) |
Integrate[Exp[- t]*BesselI[n, t], {t, 0, x}]= x*Exp[- x]*(BesselI[0, x]+ BesselI[1, x])+ n*(Exp[- x]*BesselI[0, x]- 1)+ 2*Exp[- x]*Sum[(n - k)* BesselI[k, x], {k, 1, n - 1}] |
Failure | Failure | Skip | Successful |
| 10.43.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{+ t}t^{\nu}\modBesselI{\nu}@{t}\diff{t} = \frac{e^{+ x}x^{\nu+1}}{2\nu+1}(\modBesselI{\nu}@{x}-\modBesselI{\nu+1}@{x})} | int(exp(+ t)*(t)^(nu)* BesselI(nu, t), t = 0..x)=(exp(+ x)*(x)^(nu + 1))/(2*nu + 1)*(BesselI(nu, x)- BesselI(nu + 1, x)) |
Integrate[Exp[+ t]*(t)^(\[Nu])* BesselI[\[Nu], t], {t, 0, x}]=Divide[Exp[+ x]*(x)^(\[Nu]+ 1),2*\[Nu]+ 1]*(BesselI[\[Nu], x]- BesselI[\[Nu]+ 1, x]) |
Failure | Failure | Skip | Successful |
| 10.43.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{- t}t^{\nu}\modBesselI{\nu}@{t}\diff{t} = \frac{e^{- x}x^{\nu+1}}{2\nu+1}(\modBesselI{\nu}@{x}+\modBesselI{\nu+1}@{x})} | int(exp(- t)*(t)^(nu)* BesselI(nu, t), t = 0..x)=(exp(- x)*(x)^(nu + 1))/(2*nu + 1)*(BesselI(nu, x)+ BesselI(nu + 1, x)) |
Integrate[Exp[- t]*(t)^(\[Nu])* BesselI[\[Nu], t], {t, 0, x}]=Divide[Exp[- x]*(x)^(\[Nu]+ 1),2*\[Nu]+ 1]*(BesselI[\[Nu], x]+ BesselI[\[Nu]+ 1, x]) |
Failure | Failure | Skip | Successful |
| 10.43.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{+ t}t^{-\nu}\modBesselI{\nu}@{t}\diff{t} = -\frac{e^{+ x}x^{-\nu+1}}{2\nu-1}(\modBesselI{\nu}@{x}-\modBesselI{\nu-1}@{x})-\frac{2^{-\nu+1}}{(2\nu-1)\EulerGamma@{\nu}}} | int(exp(+ t)*(t)^(- nu)* BesselI(nu, t), t = 0..x)= -(exp(+ x)*(x)^(- nu + 1))/(2*nu - 1)*(BesselI(nu, x)- BesselI(nu - 1, x))-((2)^(- nu + 1))/((2*nu - 1)* GAMMA(nu)) |
Integrate[Exp[+ t]*(t)^(- \[Nu])* BesselI[\[Nu], t], {t, 0, x}]= -Divide[Exp[+ x]*(x)^(- \[Nu]+ 1),2*\[Nu]- 1]*(BesselI[\[Nu], x]- BesselI[\[Nu]- 1, x])-Divide[(2)^(- \[Nu]+ 1),(2*\[Nu]- 1)* Gamma[\[Nu]]] |
Failure | Failure | Skip | Successful |
| 10.43.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{- t}t^{-\nu}\modBesselI{\nu}@{t}\diff{t} = -\frac{e^{- x}x^{-\nu+1}}{2\nu-1}(\modBesselI{\nu}@{x}+\modBesselI{\nu-1}@{x})+\frac{2^{-\nu+1}}{(2\nu-1)\EulerGamma@{\nu}}} | int(exp(- t)*(t)^(- nu)* BesselI(nu, t), t = 0..x)= -(exp(- x)*(x)^(- nu + 1))/(2*nu - 1)*(BesselI(nu, x)+ BesselI(nu - 1, x))+((2)^(- nu + 1))/((2*nu - 1)* GAMMA(nu)) |
Integrate[Exp[- t]*(t)^(- \[Nu])* BesselI[\[Nu], t], {t, 0, x}]= -Divide[Exp[- x]*(x)^(- \[Nu]+ 1),2*\[Nu]- 1]*(BesselI[\[Nu], x]+ BesselI[\[Nu]- 1, x])+Divide[(2)^(- \[Nu]+ 1),(2*\[Nu]- 1)* Gamma[\[Nu]]] |
Successful | Failure | - | Successful |
| 10.43.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{+ t}t^{\nu}\modBesselK{\nu}@{t}\diff{t} = \frac{e^{+ x}x^{\nu+1}}{2\nu+1}(\modBesselK{\nu}@{x}+\modBesselK{\nu+1}@{x})-\frac{2^{\nu}\EulerGamma@{\nu+1}}{2\nu+1}} | int(exp(+ t)*(t)^(nu)* BesselK(nu, t), t = 0..x)=(exp(+ x)*(x)^(nu + 1))/(2*nu + 1)*(BesselK(nu, x)+ BesselK(nu + 1, x))-((2)^(nu)* GAMMA(nu + 1))/(2*nu + 1) |
Integrate[Exp[+ t]*(t)^(\[Nu])* BesselK[\[Nu], t], {t, 0, x}]=Divide[Exp[+ x]*(x)^(\[Nu]+ 1),2*\[Nu]+ 1]*(BesselK[\[Nu], x]+ BesselK[\[Nu]+ 1, x])-Divide[(2)^(\[Nu])* Gamma[\[Nu]+ 1],2*\[Nu]+ 1] |
Failure | Failure | Skip | Error |
| 10.43.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{- t}t^{\nu}\modBesselK{\nu}@{t}\diff{t} = \frac{e^{- x}x^{\nu+1}}{2\nu+1}(\modBesselK{\nu}@{x}-\modBesselK{\nu+1}@{x})+\frac{2^{\nu}\EulerGamma@{\nu+1}}{2\nu+1}} | int(exp(- t)*(t)^(nu)* BesselK(nu, t), t = 0..x)=(exp(- x)*(x)^(nu + 1))/(2*nu + 1)*(BesselK(nu, x)- BesselK(nu + 1, x))+((2)^(nu)* GAMMA(nu + 1))/(2*nu + 1) |
Integrate[Exp[- t]*(t)^(\[Nu])* BesselK[\[Nu], t], {t, 0, x}]=Divide[Exp[- x]*(x)^(\[Nu]+ 1),2*\[Nu]+ 1]*(BesselK[\[Nu], x]- BesselK[\[Nu]+ 1, x])+Divide[(2)^(\[Nu])* Gamma[\[Nu]+ 1],2*\[Nu]+ 1] |
Failure | Failure | Skip | Error |
| 10.43.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}e^{t}t^{-\nu}\modBesselK{\nu}@{t}\diff{t} = \frac{e^{x}x^{-\nu+1}}{2\nu-1}(\modBesselK{\nu}@{x}+\modBesselK{\nu-1}@{x})} | int(exp(t)*(t)^(- nu)* BesselK(nu, t), t = x..infinity)=(exp(x)*(x)^(- nu + 1))/(2*nu - 1)*(BesselK(nu, x)+ BesselK(nu - 1, x)) |
Integrate[Exp[t]*(t)^(- \[Nu])* BesselK[\[Nu], t], {t, x, Infinity}]=Divide[Exp[x]*(x)^(- \[Nu]+ 1),2*\[Nu]- 1]*(BesselK[\[Nu], x]+ BesselK[\[Nu]- 1, x]) |
Failure | Failure | Skip | Skip |
| 10.43.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\modBesselK{\nu}@{t}\diff{t} = \tfrac{1}{2}\pi\sec@{\tfrac{1}{2}\pi\nu}} | int(BesselK(nu, t), t = 0..infinity)=(1)/(2)*Pi*sec((1)/(2)*Pi*nu) |
Integrate[BesselK[\[Nu], t], {t, 0, Infinity}]=Divide[1,2]*Pi*Sec[Divide[1,2]*Pi*\[Nu]] |
Successful | Failure | - | Successful |
| 10.43.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu-1}\modBesselK{\nu}@{t}\diff{t} = 2^{\mu-2}\EulerGamma@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu}\EulerGamma@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu}} | int((t)^(mu - 1)* BesselK(nu, t), t = 0..infinity)= (2)^(mu - 2)* GAMMA((1)/(2)*mu -(1)/(2)*nu)*GAMMA((1)/(2)*mu +(1)/(2)*nu) |
Integrate[(t)^(\[Mu]- 1)* BesselK[\[Nu], t], {t, 0, Infinity}]= (2)^(\[Mu]- 2)* Gamma[Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]]*Gamma[Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]] |
Successful | Failure | - | Successful |
| 10.43.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\cos@{at}\modBesselK{0}@{t}\diff{t} = \frac{\pi}{2(1+a^{2})^{\frac{1}{2}}}} | int(cos(a*t)*BesselK(0, t), t = 0..infinity)=(Pi)/(2*(1 + (a)^(2))^((1)/(2))) |
Integrate[Cos[a*t]*BesselK[0, t], {t, 0, Infinity}]=Divide[Pi,2*(1 + (a)^(2))^(Divide[1,2])] |
Successful | Failure | - | Successful |
| 10.43.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\sin@{at}\modBesselK{0}@{t}\diff{t} = \frac{\asinh@@{a}}{(1+a^{2})^{\frac{1}{2}}}} | int(sin(a*t)*BesselK(0, t), t = 0..infinity)=(arcsinh(a))/((1 + (a)^(2))^((1)/(2))) |
Integrate[Sin[a*t]*BesselK[0, t], {t, 0, Infinity}]=Divide[ArcSinh[a],(1 + (a)^(2))^(Divide[1,2])] |
Failure | Failure | - | Successful |
| 10.43.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu-1}e^{-at}\modBesselK{\nu}@{t}\diff{t} = \begin{cases}\left(\frac{1}{2}\pi\right)^{\frac{1}{2}}\EulerGamma@{\mu-\nu}\EulerGamma@{\mu+\nu}(1-a^{2})^{-\frac{1}{2}\mu+\frac{1}{4}}\FerrersP[-\mu+\frac{1}{2}]{\nu-\frac{1}{2}}@{a},&-1} | int((t)^(mu - 1)* exp(- a*t)*BesselK(nu, t), t = 0..infinity)= |
Integrate[(t)^(\[Mu]- 1)* Exp[- a*t]*BesselK[\[Nu], t], {t, 0, Infinity}]= |
Error | Failure | - | - |
| 10.43.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{cases}\left(\frac{1}{2}\pi\right)^{\frac{1}{2}}\EulerGamma@{\mu-\nu}\EulerGamma@{\mu+\nu}(1-a^{2})^{-\frac{1}{2}\mu+\frac{1}{4}}\FerrersP[-\mu+\frac{1}{2}]{\nu-\frac{1}{2}}@{a},&-1 < a} | |
|
Error | Failure | - | Error |
| 10.43.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\nu+1}\modBesselI{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{b^{\nu}}{(2p^{2})^{\nu+1}}\exp@{\frac{b^{2}}{4p^{2}}}} | int((t)^(nu + 1)* BesselI(nu, b*t)*exp(- (p)^(2)* (t)^(2)), t = 0..infinity)=((b)^(nu))/((2*(p)^(2))^(nu + 1))*exp(((b)^(2))/(4*(p)^(2))) |
Integrate[(t)^(\[Nu]+ 1)* BesselI[\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}]=Divide[(b)^(\[Nu]),(2*(p)^(2))^(\[Nu]+ 1)]*Exp[Divide[(b)^(2),4*(p)^(2)]] |
Failure | Failure | Skip | Error |
| 10.43.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\modBesselI{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{\sqrt{\pi}}{2p}\exp@{\frac{b^{2}}{8p^{2}}}\modBesselI{\frac{1}{2}\nu}@{\frac{b^{2}}{8p^{2}}}} | int(BesselI(nu, b*t)*exp(- (p)^(2)* (t)^(2)), t = 0..infinity)=(sqrt(Pi))/(2*p)*exp(((b)^(2))/(8*(p)^(2)))*BesselI((1)/(2)*nu, ((b)^(2))/(8*(p)^(2))) |
Integrate[BesselI[\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}]=Divide[Sqrt[Pi],2*p]*Exp[Divide[(b)^(2),8*(p)^(2)]]*BesselI[Divide[1,2]*\[Nu], Divide[(b)^(2),8*(p)^(2)]] |
Failure | Failure | Skip | Error |
| 10.43.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\modBesselK{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{\sqrt{\pi}}{4p}\sec@{\tfrac{1}{2}\pi\nu}\exp@{\frac{b^{2}}{8p^{2}}}\modBesselK{\frac{1}{2}\nu}@{\frac{b^{2}}{8p^{2}}}} | int(BesselK(nu, b*t)*exp(- (p)^(2)* (t)^(2)), t = 0..infinity)=(sqrt(Pi))/(4*p)*sec((1)/(2)*Pi*nu)*exp(((b)^(2))/(8*(p)^(2)))*BesselK((1)/(2)*nu, ((b)^(2))/(8*(p)^(2))) |
Integrate[BesselK[\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}]=Divide[Sqrt[Pi],4*p]*Sec[Divide[1,2]*Pi*\[Nu]]*Exp[Divide[(b)^(2),8*(p)^(2)]]*BesselK[Divide[1,2]*\[Nu], Divide[(b)^(2),8*(p)^(2)]] |
Failure | Failure | Skip | Error |
| 10.43.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{\modBesselK{\mu}@{at}\BesselJ{\nu}@{bt}}{t^{\lambda}}\diff{t} = \frac{b^{\nu}\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\lambda+\frac{1}{2}\mu+\frac{1}{2}}\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\lambda-\frac{1}{2}\mu+\frac{1}{2}}}{2^{\lambda+1}a^{\nu-\lambda+1}}\*\hyperOlverF@{\frac{\nu-\lambda+\mu+1}{2}}{\frac{\nu-\lambda-\mu+1}{2}}{\nu+1}{-\frac{b^{2}}{a^{2}}}} | int((BesselK(mu, a*t)*BesselJ(nu, b*t))/((t)^(lambda)), t = 0..infinity)=((b)^(nu)* GAMMA((1)/(2)*nu -(1)/(2)*lambda +(1)/(2)*mu +(1)/(2))*GAMMA((1)/(2)*nu -(1)/(2)*lambda -(1)/(2)*mu +(1)/(2)))/((2)^(lambda + 1)* (a)^(nu - lambda + 1))* hypergeom([(nu - lambda + mu + 1)/(2), (nu - lambda - mu + 1)/(2)], [nu + 1], -((b)^(2))/((a)^(2)))/GAMMA(nu + 1) |
Integrate[Divide[BesselK[\[Mu], a*t]*BesselJ[\[Nu], b*t],(t)^(\[Lambda])], {t, 0, Infinity}]=Divide[(b)^(\[Nu])* Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Lambda]+Divide[1,2]*\[Mu]+Divide[1,2]]*Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Lambda]-Divide[1,2]*\[Mu]+Divide[1,2]],(2)^(\[Lambda]+ 1)* (a)^(\[Nu]- \[Lambda]+ 1)]* Hypergeometric2F1Regularized[Divide[\[Nu]- \[Lambda]+ \[Mu]+ 1,2], Divide[\[Nu]- \[Lambda]- \[Mu]+ 1,2], \[Nu]+ 1, -Divide[(b)^(2),(a)^(2)]] |
Error | Failure | - | Error |
| 10.43.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu+\nu+1}\modBesselK{\mu}@{at}\BesselJ{\nu}@{bt}\diff{t} = \frac{(2a)^{\mu}(2b)^{\nu}\EulerGamma@{\mu+\nu+1}}{(a^{2}+b^{2})^{\mu+\nu+1}}} | int((t)^(mu + nu + 1)* BesselK(mu, a*t)*BesselJ(nu, b*t), t = 0..infinity)=((2*a)^(mu)*(2*b)^(nu)* GAMMA(mu + nu + 1))/(((a)^(2)+ (b)^(2))^(mu + nu + 1)) |
Integrate[(t)^(\[Mu]+ \[Nu]+ 1)* BesselK[\[Mu], a*t]*BesselJ[\[Nu], b*t], {t, 0, Infinity}]=Divide[(2*a)^(\[Mu])*(2*b)^(\[Nu])* Gamma[\[Mu]+ \[Nu]+ 1],((a)^(2)+ (b)^(2))^(\[Mu]+ \[Nu]+ 1)] |
Error | Failure | - | Error |
| 10.43.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t\exp@{-p^{2}t^{2}}\modBesselI{\nu}@{at}\modBesselI{\nu}@{bt}\diff{t} = \frac{1}{2p^{2}}\exp@{\frac{a^{2}+b^{2}}{4p^{2}}}\modBesselI{\nu}@{\frac{ab}{2p^{2}}}} | int(t*exp(- (p)^(2)* (t)^(2))*BesselI(nu, a*t)*BesselI(nu, b*t), t = 0..infinity)=(1)/(2*(p)^(2))*exp(((a)^(2)+ (b)^(2))/(4*(p)^(2)))*BesselI(nu, (a*b)/(2*(p)^(2))) |
Integrate[t*Exp[- (p)^(2)* (t)^(2)]*BesselI[\[Nu], a*t]*BesselI[\[Nu], b*t], {t, 0, Infinity}]=Divide[1,2*(p)^(2)]*Exp[Divide[(a)^(2)+ (b)^(2),4*(p)^(2)]]*BesselI[\[Nu], Divide[a*b,2*(p)^(2)]] |
Failure | Failure | Skip | Error |
| 10.43.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t\exp@{-p^{2}t^{2}}\modBesselI{0}@{at}\modBesselK{0}@{at}\diff{t} = \frac{1}{4p^{2}}\exp@{\frac{a^{2}}{2p^{2}}}\modBesselK{0}@{\frac{a^{2}}{2p^{2}}}} | int(t*exp(- (p)^(2)* (t)^(2))*BesselI(0, a*t)*BesselK(0, a*t), t = 0..infinity)=(1)/(4*(p)^(2))*exp(((a)^(2))/(2*(p)^(2)))*BesselK(0, ((a)^(2))/(2*(p)^(2))) |
Integrate[t*Exp[- (p)^(2)* (t)^(2)]*BesselI[0, a*t]*BesselK[0, a*t], {t, 0, Infinity}]=Divide[1,4*(p)^(2)]*Exp[Divide[(a)^(2),2*(p)^(2)]]*BesselK[0, Divide[(a)^(2),2*(p)^(2)]] |
Failure | Failure | Skip | Error |
| 10.44#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \sum_{k=0}^{\infty}\frac{z^{k}}{k!}\BesselJ{\nu+k}@{z}} | BesselI(nu, z)= sum(((z)^(k))/(factorial(k))*BesselJ(nu + k, z), k = 0..infinity) |
BesselI[\[Nu], z]= Sum[Divide[(z)^(k),(k)!]*BesselJ[\[Nu]+ k, z], {k, 0, Infinity}] |
Failure | Successful | Skip | - |
| 10.44#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \!\BesselJ{\nu}@{z} = \sum_{k=0}^{\infty}(-1)^{k}\frac{z^{k}}{k!}\modBesselI{\nu+k}@{z}} | BesselJ(nu, z)= sum((- 1)^(k)*((z)^(k))/(factorial(k))*BesselI(nu + k, z), k = 0..infinity) |
BesselJ[\[Nu], z]= Sum[(- 1)^(k)*Divide[(z)^(k),(k)!]*BesselI[\[Nu]+ k, z], {k, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 10.44.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\tfrac{1}{2}z\right)^{\nu} = \sum_{k=0}^{\infty}(-1)^{k}\frac{(\nu+2k)\EulerGamma@{\nu+k}}{k!}\modBesselI{\nu+2k}@{z}} | ((1)/(2)*z)^(nu)= sum((- 1)^(k)*((nu + 2*k)* GAMMA(nu + k))/(factorial(k))*BesselI(nu + 2*k, z), k = 0..infinity) |
(Divide[1,2]*z)^(\[Nu])= Sum[(- 1)^(k)*Divide[(\[Nu]+ 2*k)* Gamma[\[Nu]+ k],(k)!]*BesselI[\[Nu]+ 2*k, z], {k, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 10.44.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{0}@{z} = -\left(\ln@{\tfrac{1}{2}z}+\EulerConstant\right)\modBesselI{0}@{z}+2\sum_{k=1}^{\infty}\frac{\modBesselI{2k}@{z}}{k}} | BesselK(0, z)= -(ln((1)/(2)*z)+ gamma)* BesselI(0, z)+ 2*sum((BesselI(2*k, z))/(k), k = 1..infinity) |
BesselK[0, z]= -(Log[Divide[1,2]*z]+ EulerGamma)* BesselI[0, z]+ 2*Sum[Divide[BesselI[2*k, z],k], {k, 1, Infinity}] |
Failure | Successful | Skip | - |
| 10.44.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{n}@{z} = \frac{n!(\tfrac{1}{2}z)^{-n}}{2}\sum_{k=0}^{n-1}(-1)^{k}\frac{(\tfrac{1}{2}z)^{k}\modBesselI{k}@{z}}{k!(n-k)}+(-1)^{n-1}\left(\ln@{\tfrac{1}{2}z}-\digamma@{n+1}\right)\modBesselI{n}@{z}+(-1)^{n}\sum_{k=1}^{\infty}\frac{(n+2k)\modBesselI{n+2k}@{z}}{k(n+k)}} | BesselK(n, z)=(factorial(n)*((1)/(2)*z)^(- n))/(2)*sum((- 1)^(k)*(((1)/(2)*z)^(k)* BesselI(k, z))/(factorial(k)*(n - k)), k = 0..n - 1)+(- 1)^(n - 1)*(ln((1)/(2)*z)- Psi(n + 1))* BesselI(n, z)+(- 1)^(n)* sum(((n + 2*k)* BesselI(n + 2*k, z))/(k*(n + k)), k = 1..infinity) |
BesselK[n, z]=Divide[(n)!*(Divide[1,2]*z)^(- n),2]*Sum[(- 1)^(k)*Divide[(Divide[1,2]*z)^(k)* BesselI[k, z],(k)!*(n - k)], {k, 0, n - 1}]+(- 1)^(n - 1)*(Log[Divide[1,2]*z]- PolyGamma[n + 1])* BesselI[n, z]+(- 1)^(n)* Sum[Divide[(n + 2*k)* BesselI[n + 2*k, z],k*(n + k)], {k, 1, Infinity}] |
Failure | Failure | Skip | Skip |
| 10.45.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{2}\deriv[2]{w}{x}+x\deriv{w}{x}+(\nu^{2}-x^{2})w = 0} | (x)^(2)* diff(w, [x$(2)])+ x*diff(w, x)+((nu)^(2)- (x)^(2))* w = 0 |
(x)^(2)* D[w, {x, 2}]+ x*D[w, x]+((\[Nu])^(2)- (x)^(2))* w = 0 |
Failure | Failure | Fail -7.071067807+4.242640683*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), x = 1}-11.31370849-.2828427124e-8*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), x = 2}-18.38477630-7.071067813*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), x = 3}4.242640683+7.071067807*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[-7.0710678118654755, 4.242640687119286] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-11.313708498984761 <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-18.38477631085024, -7.0710678118654755] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.242640687119286, -7.0710678118654755] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.45.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modBesselIimag{\nu}@{x} = \realpart@@{(\modBesselI{i\nu}@{x})}} | Re(BesselI(I*(nu), x))= Re(BesselI(I*nu, x)) |
Re[BesselI[I*\[Nu], x]]= Re[BesselI[I*\[Nu], x]] |
Successful | Successful | - | - |
| 10.45.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modBesselKimag{\nu}@{x} = \modBesselK{i\nu}@{x}} | BesselK(I*(nu), x)= BesselK(I*nu, x) |
BesselK[I*\[Nu], x]= BesselK[I*\[Nu], x] |
Successful | Successful | - | - |
| 10.45.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modBesselKimag{\nu}@{x},\modBesselIimag{\nu}@{x}} = 1/x} | (BesselK(I*(nu), x))*diff(Re(BesselI(I*(nu), x)), x)-diff(BesselK(I*(nu), x), x)*(Re(BesselI(I*(nu), x)))= 1/ x |
Wronskian[{BesselK[I*\[Nu], x], Re[BesselI[I*\[Nu], x]]}, x]= 1/ x |
Failure | Failure | Error | Successful |
| 10.45.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselKimag{0}@{x} = \modBesselK{0}@{x}} | BesselK(I*(0), x)= BesselK(0, x) |
BesselK[I*0, x]= BesselK[0, x] |
Successful | Successful | - | - |
| 10.47.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{2}\deriv[2]{w}{z}+2z\deriv{w}{z}+\left(z^{2}-n(n+1)\right)w = 0} | (z)^(2)* diff(w, [z$(2)])+ 2*z*diff(w, z)+((z)^(2)- n*(n + 1))* w = 0 |
(z)^(2)* D[w, {z, 2}]+ 2*z*D[w, z]+((z)^(2)- n*(n + 1))* w = 0 |
Failure | Failure | Fail -8.485281369+2.828427121*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}-14.14213562-2.828427127*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}-22.62741699-11.31370850*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}2.828427121-8.485281369*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Fail
Complex[-8.485281374238571, 2.8284271247461903] <- {Rule[n, 1], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-14.142135623730951, -2.8284271247461903] <- {Rule[n, 2], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-22.627416997969522, -11.313708498984761] <- {Rule[n, 3], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.8284271247461903, -8.485281374238571] <- {Rule[n, 1], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.47.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{2}\deriv[2]{w}{z}+2z\deriv{w}{z}-\left(z^{2}+n(n+1)\right)w = 0} | (z)^(2)* diff(w, [z$(2)])+ 2*z*diff(w, z)-((z)^(2)+ n*(n + 1))* w = 0 |
(z)^(2)* D[w, {z, 2}]+ 2*z*D[w, z]-((z)^(2)+ n*(n + 1))* w = 0 |
Failure | Failure | Fail 2.828427121-8.485281369*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}-2.828427127-14.14213562*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}-11.31370850-22.62741699*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}-8.485281369+2.828427121*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Fail
Complex[2.8284271247461903, -8.485281374238571] <- {Rule[n, 1], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.8284271247461903, -14.142135623730951] <- {Rule[n, 2], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-11.313708498984761, -22.627416997969522] <- {Rule[n, 3], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-8.485281374238571, 2.8284271247461903] <- {Rule[n, 1], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.47.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\BesselJ{n+\frac{1}{2}}@{z}} | Error |
SphericalBesselJ[n, z]=Sqrt[Divide[1,2]*Pi/ z]*BesselJ[n +Divide[1,2], z] |
Error | Failure | - | Successful |
| 10.47.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\tfrac{1}{2}\pi/z}\BesselJ{n+\frac{1}{2}}@{z} = (-1)^{n}\sqrt{\tfrac{1}{2}\pi/z}\BesselY{-n-\frac{1}{2}}@{z}} | sqrt((1)/(2)*Pi/ z)*BesselJ(n +(1)/(2), z)=(- 1)^(n)*sqrt((1)/(2)*Pi/ z)*BesselY(- n -(1)/(2), z) |
Sqrt[Divide[1,2]*Pi/ z]*BesselJ[n +Divide[1,2], z]=(- 1)^(n)*Sqrt[Divide[1,2]*Pi/ z]*BesselY[- n -Divide[1,2], z] |
Failure | Failure | Successful | Successful |
| 10.47.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\BesselY{n+\frac{1}{2}}@{z}} | Error |
SphericalBesselY[n, z]=Sqrt[Divide[1,2]*Pi/ z]*BesselY[n +Divide[1,2], z] |
Error | Failure | - | Successful |
| 10.47.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\tfrac{1}{2}\pi/z}\BesselY{n+\frac{1}{2}}@{z} = (-1)^{n+1}\sqrt{\tfrac{1}{2}\pi/z}\BesselJ{-n-\frac{1}{2}}@{z}} | sqrt((1)/(2)*Pi/ z)*BesselY(n +(1)/(2), z)=(- 1)^(n + 1)*sqrt((1)/(2)*Pi/ z)*BesselJ(- n -(1)/(2), z) |
Sqrt[Divide[1,2]*Pi/ z]*BesselY[n +Divide[1,2], z]=(- 1)^(n + 1)*Sqrt[Divide[1,2]*Pi/ z]*BesselJ[- n -Divide[1,2], z] |
Failure | Failure | Successful | Successful |
| 10.47.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{1}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\HankelH{1}{n+\frac{1}{2}}@{z}} | Error |
\|SphericalHankelH2[1, n]* z =Sqrt[Divide[1,2]*Pi/ z]*HankelH1[n +Divide[1,2], z] | Error | Failure | - | Error |
| 10.47.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\tfrac{1}{2}\pi/z}\HankelH{1}{n+\frac{1}{2}}@{z} = (-1)^{n+1}\iunit\sqrt{\tfrac{1}{2}\pi/z}\HankelH{1}{-n-\frac{1}{2}}@{z}} | sqrt((1)/(2)*Pi/ z)*HankelH1(n +(1)/(2), z)=(- 1)^(n + 1)* I*sqrt((1)/(2)*Pi/ z)*HankelH1(- n -(1)/(2), z) |
Sqrt[Divide[1,2]*Pi/ z]*HankelH1[n +Divide[1,2], z]=(- 1)^(n + 1)* I*Sqrt[Divide[1,2]*Pi/ z]*HankelH1[- n -Divide[1,2], z] |
Failure | Failure | Successful | Successful |
| 10.47.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{2}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\HankelH{2}{n+\frac{1}{2}}@{z}} | Error |
\|SphericalHankelH2[2, n]* z =Sqrt[Divide[1,2]*Pi/ z]*HankelH2[n +Divide[1,2], z] | Error | Failure | - | Error |
| 10.47.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\tfrac{1}{2}\pi/z}\HankelH{2}{n+\frac{1}{2}}@{z} = (-1)^{n}\iunit\sqrt{\tfrac{1}{2}\pi/z}\HankelH{2}{-n-\frac{1}{2}}@{z}} | sqrt((1)/(2)*Pi/ z)*HankelH2(n +(1)/(2), z)=(- 1)^(n)* I*sqrt((1)/(2)*Pi/ z)*HankelH2(- n -(1)/(2), z) |
Sqrt[Divide[1,2]*Pi/ z]*HankelH2[n +Divide[1,2], z]=(- 1)^(n)* I*Sqrt[Divide[1,2]*Pi/ z]*HankelH2[- n -Divide[1,2], z] |
Failure | Failure | Successful | Successful |
| 10.47.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselI{n+\frac{1}{2}}@{z}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z =Sqrt[Divide[1,2]*Pi/ z]*BesselI[n +Divide[1,2], z] | Error | Error | - | - |
| 10.47.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselI{-n-\frac{1}{2}}@{z}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z =Sqrt[Divide[1,2]*Pi/ z]*BesselI[- n -Divide[1,2], z] | Error | Error | - | - |
| 10.47.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselK{n+\frac{1}{2}}@{z}} | Error |
Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]=Sqrt[Divide[1,2]*Pi/ z]*BesselK[n +Divide[1,2], z] |
Error | Successful | - | - |
| 10.47.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\tfrac{1}{2}\pi/z}\modBesselK{n+\frac{1}{2}}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselK{-n-\frac{1}{2}}@{z}} | sqrt((1)/(2)*Pi/ z)*BesselK(n +(1)/(2), z)=sqrt((1)/(2)*Pi/ z)*BesselK(- n -(1)/(2), z) |
Sqrt[Divide[1,2]*Pi/ z]*BesselK[n +Divide[1,2], z]=Sqrt[Divide[1,2]*Pi/ z]*BesselK[- n -Divide[1,2], z] |
Successful | Successful | - | - |
| 10.47#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{1}{n}@{z} = \sphBesselJ{n}@{z}+i\sphBesselY{n}@{z}} | Error |
\|SphericalHankelH2[1, n]* z = SphericalBesselJ[n, z]+ I*SphericalBesselY[n, z] | Error | Failure | - | Error |
| 10.47#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{2}{n}@{z} = \sphBesselJ{n}@{z}-i\sphBesselY{n}@{z}} | Error |
\|SphericalHankelH2[2, n]* z = SphericalBesselJ[n, z]- I*SphericalBesselY[n, z] | Error | Failure | - | Error |
| 10.47.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = (-1)^{n+1}\tfrac{1}{2}\pi\left(\modsphBesseli{1}{n}@{z}-\modsphBesseli{2}{n}@{z}\right)} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z - Sqrt[1/2 Pi /$2] BesselI[(-1)^(2-1)*n + 1/2, n]\|\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z) | Error | Error | - | - |
| 10.47#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{n}@{z} = i^{-n}\sphBesselJ{n}@{iz}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z = (I)^(- n)* SphericalBesselJ[n, I*z] | Error | Error | - | - |
| 10.47#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{n}@{z} = i^{-n-1}\sphBesselY{n}@{iz}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z = (I)^(- n - 1)* SphericalBesselY[n, I*z] | Error | Error | - | - |
| 10.47.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = -\tfrac{1}{2}\pi i^{n}\sphHankelh{1}{n}@{iz}} | Error |
\|SphericalHankelH2[1, n]*I*z | Error | Failure | - | Error |
| 10.47.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}\pi i^{n}\sphHankelh{1}{n}@{iz} = -\tfrac{1}{2}\pi i^{-n}\sphHankelh{2}{n}@{-iz}} | Error |
\|SphericalHankelH2[1, n]*I*z*= -Divide[1,2]*Pi*(I)^(- n)* SphericalHankelH1[2, n]\|\|SphericalHankelH2[2, n]*- I*z | Error | Failure | - | Error |
| 10.47.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{-z} = -\tfrac{1}{2}\pi\left(\modsphBesseli{1}{n}@{z}+\modsphBesseli{2}{n}@{z}\right)} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z + Sqrt[1/2 Pi /$2] BesselI[(-1)^(2-1)*n + 1/2, n]\|\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z) | Error | Error | - | - |
| 10.49.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = \sin@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{n/2}}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+1}}+\cos@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{(n-1)/2}}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+2}}} | Error |
SphericalBesselJ[n, z]= Sin[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k]*(n +Divide[1,2]),(z)^(2*k + 1)], {k, 0, Floor[n/ 2]}]+ Cos[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k + 1]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, Floor[(n - 1)/ 2]}] |
Error | Failure | - | Skip |
| 10.49#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{0}@{z} = \frac{\sin@@{z}}{z}} | Error |
SphericalBesselJ[0, z]=Divide[Sin[z],z] |
Error | Successful | - | - |
| 10.49#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{1}@{z} = \frac{\sin@@{z}}{z^{2}}-\frac{\cos@@{z}}{z}} | Error |
SphericalBesselJ[1, z]=Divide[Sin[z],(z)^(2)]-Divide[Cos[z],z] |
Error | Successful | - | - |
| 10.49#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{2}@{z} = \left(-\frac{1}{z}+\frac{3}{z^{3}}\right)\sin@@{z}-\frac{3}{z^{2}}\cos@@{z}} | Error |
SphericalBesselJ[2, z]=(-Divide[1,z]+Divide[3,(z)^(3)])* Sin[z]-Divide[3,(z)^(2)]*Cos[z] |
Error | Successful | - | - |
| 10.49.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{n}@{z} = -\cos@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{n/2}}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+1}}+\sin@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{(n-1)/2}}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+2}}} | Error |
SphericalBesselY[n, z]= - Cos[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k]*(n +Divide[1,2]),(z)^(2*k + 1)], {k, 0, Floor[n/ 2]}]+ Sin[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k + 1]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, Floor[(n - 1)/ 2]}] |
Error | Failure | - | Skip |
| 10.49#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{0}@{z} = -\frac{\cos@@{z}}{z}} | Error |
SphericalBesselY[0, z]= -Divide[Cos[z],z] |
Error | Successful | - | - |
| 10.49#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{1}@{z} = -\frac{\cos@@{z}}{z^{2}}-\frac{\sin@@{z}}{z}} | Error |
SphericalBesselY[1, z]= -Divide[Cos[z],(z)^(2)]-Divide[Sin[z],z] |
Error | Successful | - | - |
| 10.49#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{2}@{z} = \left(\frac{1}{z}-\frac{3}{z^{3}}\right)\cos@@{z}-\frac{3}{z^{2}}\sin@@{z}} | Error |
SphericalBesselY[2, z]=(Divide[1,z]-Divide[3,(z)^(3)])* Cos[z]-Divide[3,(z)^(2)]*Sin[z] |
Error | Successful | - | - |
| 10.49.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{1}{n}@{z} = e^{iz}\sum_{k=0}^{n}i^{k-n-1}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}} | Error |
\|SphericalHankelH2[1, n]* z = Exp[I*z]*Sum[(I)^(k - n - 1)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}] | Error | Failure | - | Error |
| 10.49.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{2}{n}@{z} = e^{-iz}\sum_{k=0}^{n}(-i)^{k-n-1}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}} | Error |
\|SphericalHankelH2[2, n]* z = Exp[- I*z]*Sum[(- I)^(k - n - 1)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}] | Error | Failure | - | Error |
| 10.49.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{n}@{z} = \tfrac{1}{2}e^{z}\sum_{k=0}^{n}(-1)^{k}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}+(-1)^{n+1}\*\tfrac{1}{2}e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z =Divide[1,2]*Exp[z]*Sum[(- 1)^(k)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}]+(- 1)^(n + 1)*Divide[1,2]*(E)^(- z)* Sum[Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}] | Error | Error | - | - |
| 10.49#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{0}@{z} = \frac{\sinh@@{z}}{z}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-0 - 1/2, 0]* z =Divide[Sinh[z],z] | Error | Error | - | - |
| 10.49#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{1}@{z} = -\frac{\sinh@@{z}}{z^{2}}+\frac{\cosh@@{z}}{z}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-1 - 1/2, 1]* z = -Divide[Sinh[z],(z)^(2)]+Divide[Cosh[z],z] | Error | Error | - | - |
| 10.49#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{2}@{z} = \left(\frac{1}{z}+\frac{3}{z^{3}}\right)\sinh@@{z}-\frac{3}{z^{2}}\cosh@@{z}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-2 - 1/2, 2]* z =(Divide[1,z]+Divide[3,(z)^(3)])* Sinh[z]-Divide[3,(z)^(2)]*Cosh[z] | Error | Error | - | - |
| 10.49.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{n}@{z} = \tfrac{1}{2}e^{z}\sum_{k=0}^{n}(-1)^{k}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}+(-1)^{n}\tfrac{1}{2}e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z =Divide[1,2]*Exp[z]*Sum[(- 1)^(k)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}]+(- 1)^(n)*Divide[1,2]*(E)^(- z)* Sum[Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}] | Error | Error | - | - |
| 10.49#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{0}@{z} = \frac{\cosh@@{z}}{z}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-0 - 1/2, 0]* z =Divide[Cosh[z],z] | Error | Error | - | - |
| 10.49#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{1}@{z} = -\frac{\cosh@@{z}}{z^{2}}+\frac{\sinh@@{z}}{z}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-1 - 1/2, 1]* z = -Divide[Cosh[z],(z)^(2)]+Divide[Sinh[z],z] | Error | Error | - | - |
| 10.49#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{2}@{z} = \left(\frac{1}{z}+\frac{3}{z^{3}}\right)\cosh@@{z}-\frac{3}{z^{2}}\sinh@@{z}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-2 - 1/2, 2]* z =(Divide[1,z]+Divide[3,(z)^(3)])* Cosh[z]-Divide[3,(z)^(2)]*Sinh[z] | Error | Error | - | - |
| 10.49.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = \tfrac{1}{2}\pi e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}} | Error |
Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]=Divide[1,2]*Pi*Exp[- z]*Sum[Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}] |
Error | Failure | - | Skip |
| 10.49#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{0}@{z} = \tfrac{1}{2}\pi\frac{e^{-z}}{z}} | Error |
Sqrt[1/2 Pi /z] BesselK[0 + 1/2, z]=Divide[1,2]*Pi*Divide[Exp[- z],z] |
Error | Failure | - | Successful |
| 10.49#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{1}@{z} = \tfrac{1}{2}\pi e^{-z}\left(\frac{1}{z}+\frac{1}{z^{2}}\right)} | Error |
Sqrt[1/2 Pi /z] BesselK[1 + 1/2, z]=Divide[1,2]*Pi*Exp[- z]*(Divide[1,z]+Divide[1,(z)^(2)]) |
Error | Failure | - | Successful |
| 10.49#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{2}@{z} = \tfrac{1}{2}\pi e^{-z}\left(\frac{1}{z}+\frac{3}{z^{2}}+\frac{3}{z^{3}}\right)} | Error |
Sqrt[1/2 Pi /z] BesselK[2 + 1/2, z]=Divide[1,2]*Pi*Exp[- z]*(Divide[1,z]+Divide[3,(z)^(2)]+Divide[3,(z)^(3)]) |
Error | Failure | - | Successful |
| 10.49.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}^{2}@{z}+\sphBesselY{n}^{2}@{z} = \sum_{k=0}^{n}\frac{s_{k}(n+\frac{1}{2})}{z^{2k+2}}} | Error |
(SphericalBesselJ[n, z])^(2)+ (SphericalBesselY[n, z])^(2)= Sum[Divide[Subscript[s, k]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, n}] |
Error | Failure | - | Successful |
| 10.49#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{0}^{2}@{z}+\sphBesselY{0}^{2}@{z} = z^{-2}} | Error |
(SphericalBesselJ[0, z])^(2)+ (SphericalBesselY[0, z])^(2)= (z)^(- 2) |
Error | Successful | - | - |
| 10.49#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{1}^{2}@{z}+\sphBesselY{1}^{2}@{z} = z^{-2}+z^{-4}} | Error |
(SphericalBesselJ[1, z])^(2)+ (SphericalBesselY[1, z])^(2)= (z)^(- 2)+ (z)^(- 4) |
Error | Successful | - | - |
| 10.49#Ex22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{2}^{2}@{z}+\sphBesselY{2}^{2}@{z} = z^{-2}+3z^{-4}+9z^{-6}} | Error |
(SphericalBesselJ[2, z])^(2)+ (SphericalBesselY[2, z])^(2)= (z)^(- 2)+ 3*(z)^(- 4)+ 9*(z)^(- 6) |
Error | Successful | - | - |
| 10.49.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\modsphBesseli{1}{n}@{z}\right)^{2}-\left(\modsphBesseli{2}{n}@{z}\right)^{2} = (-1)^{n+1}\sum_{k=0}^{n}(-1)^{k}\frac{s_{k}(n+\frac{1}{2})}{z^{2k+2}}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z))^(2)-((Sqrt[1/2 Pi /$2] BesselI[(-1)^(2-1)*n + 1/2, n]\|\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z))^(2)=(- 1)^(n + 1)* Sum[(- 1)^(k)*Divide[Subscript[s, k]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, n}] | Error | Error | - | - |
| 10.50#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\sphBesselJ{n}@{z},\sphBesselY{n}@{z}} = z^{-2}} | Error |
Wronskian[{SphericalBesselJ[n, z], SphericalBesselY[n, z]}, z]= (z)^(- 2) |
Error | Successful | - | - |
| 10.50#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\sphHankelh{1}{n}@{z},\sphHankelh{2}{n}@{z}} = -2iz^{-2}} | Error |
\|SphericalHankelH2[1, n]* z, SphericalHankelH1[2, n]\|\|SphericalHankelH2[2, n]* z}, z]= - 2*I*(z)^(- 2) | Error | Failure | - | Error |
| 10.50#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modsphBesseli{1}{n}@{z},\modsphBesseli{2}{n}@{z}} = (-1)^{n+1}z^{-2}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z] BesselI[(-1)^(1-1)*n + 1/2, n]\|\|Sqrt[1/2 Pi /Sqrt[1/2 Pi /$2] BesselI[(-1)^(2-1)*n + 1/2, n]\|\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z] BesselI[-n - 1/2, n]* z, Sqrt[1/2 Pi /$2] BesselI[(-1)^(2-1)*n + 1/2, n]\|\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z}, z]=(- 1)^(n + 1)* (z)^(- 2) | Error | Error | - | - |
| 10.50#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modsphBesseli{2}{n}@{z},\modsphBesselK{n}@{z}}\\ = -\tfrac{1}{2}\pi z^{-2}} | Error |
\|Sqrt[1/2 Pi /Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]] BesselI[-n - 1/2, n]* z, Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]}, z]= -Divide[1,2]*Pi*(z)^(- 2) | Error | Error | - | - |
| 10.50#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n+1}@{z}\sphBesselY{n}@{z}-\sphBesselJ{n}@{z}\sphBesselY{n+1}@{z} = z^{-2}} | Error |
SphericalBesselJ[n + 1, z]*SphericalBesselY[n, z]- SphericalBesselJ[n, z]*SphericalBesselY[n + 1, z]= (z)^(- 2) |
Error | Successful | - | - |
| 10.50#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n+2}@{z}\sphBesselY{n}@{z}-\sphBesselJ{n}@{z}\sphBesselY{n+2}@{z} = (2n+3)z^{-3}} | Error |
SphericalBesselJ[n + 2, z]*SphericalBesselY[n, z]- SphericalBesselJ[n, z]*SphericalBesselY[n + 2, z]=(2*n + 3)* (z)^(- 3) |
Error | Failure | - | Successful |
| 10.50.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{0}@{z}\sphBesselJ{n}@{z}+\sphBesselY{0}@{z}\sphBesselY{n}@{z} = \cos@{\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{n/2}}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+2}}+\sin@{\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{(n-1)/2}}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+3}}} | Error |
SphericalBesselJ[0, z]*SphericalBesselJ[n, z]+ SphericalBesselY[0, z]*SphericalBesselY[n, z]= Cos[Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, Floor[n/ 2]}]+ Sin[Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k + 1]*(n +Divide[1,2]),(z)^(2*k + 3)], {k, 0, Floor[(n - 1)/ 2]}] |
Error | Failure | - | Skip |
| 10.53.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = z^{n}\sum_{k=0}^{\infty}\frac{(-\frac{1}{2}z^{2})^{k}}{k!(2n+2k+1)!!}} | Error |
SphericalBesselJ[n, z]= (z)^(n)* Sum[Divide[(-Divide[1,2]*(z)^(2))^(k),(k)!*(2*n + 2*k + 1)!!], {k, 0, Infinity}] |
Error | Failure | - | Successful |
| 10.53.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{n}@{z} = -\frac{1}{z^{n+1}}\sum_{k=0}^{n}\frac{(2n-2k-1)!!(\frac{1}{2}z^{2})^{k}}{k!}+\frac{(-1)^{n+1}}{z^{n+1}}\sum_{k=n+1}^{\infty}\frac{(-\frac{1}{2}z^{2})^{k}}{k!(2k-2n-1)!!}} | Error |
SphericalBesselY[n, z]= -Divide[1,(z)^(n + 1)]*Sum[Divide[(2*n - 2*k - 1)!!*(Divide[1,2]*(z)^(2))^(k),(k)!], {k, 0, n}]+Divide[(- 1)^(n + 1),(z)^(n + 1)]*Sum[Divide[(-Divide[1,2]*(z)^(2))^(k),(k)!*(2*k - 2*n - 1)!!], {k, n + 1, Infinity}] |
Error | Failure | - | Successful |
| 10.53.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{n}@{z} = z^{n}\sum_{k=0}^{\infty}\frac{(\frac{1}{2}z^{2})^{k}}{k!(2n+2k+1)!!}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z = (z)^(n)* Sum[Divide[(Divide[1,2]*(z)^(2))^(k),(k)!*(2*n + 2*k + 1)!!], {k, 0, Infinity}] | Error | Error | - | - |
| 10.53.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{n}@{z} = \frac{(-1)^{n}}{z^{n+1}}\sum_{k=0}^{n}\frac{(2n-2k-1)!!(-\frac{1}{2}z^{2})^{k}}{k!}+\frac{1}{z^{n+1}}\sum_{k=n+1}^{\infty}\frac{(\frac{1}{2}z^{2})^{k}}{k!(2k-2n-1)!!}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z =Divide[(- 1)^(n),(z)^(n + 1)]*Sum[Divide[(2*n - 2*k - 1)!!*(-Divide[1,2]*(z)^(2))^(k),(k)!], {k, 0, n}]+Divide[1,(z)^(n + 1)]*Sum[Divide[(Divide[1,2]*(z)^(2))^(k),(k)!*(2*k - 2*n - 1)!!], {k, n + 1, Infinity}] | Error | Error | - | - |
| 10.54.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = \frac{z^{n}}{2^{n+1}n!}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}(\sin@@{\theta})^{2n+1}\diff{\theta}} | Error |
SphericalBesselJ[n, z]=Divide[(z)^(n),(2)^(n + 1)* (n)!]*Integrate[Cos[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*n + 1), {\[Theta], 0, Pi}] |
Error | Failure | - | Successful |
| 10.54.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = \frac{(-i)^{n}}{2}\int_{0}^{\pi}e^{iz\cos@@{\theta}}\assLegendreP[]{n}@{\cos@@{\theta}}\sin@@{\theta}\diff{\theta}} | Error |
SphericalBesselJ[n, z]=Divide[(- I)^(n),2]*Integrate[Exp[I*z*Cos[\[Theta]]]*LegendreP[n, 0, 3, Cos[\[Theta]]]*Sin[\[Theta]], {\[Theta], 0, Pi}] |
Error | Failure | - | Error |
| 10.54.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = \frac{\pi}{2}\int_{1}^{\infty}e^{-zt}\assLegendreP[]{n}@{t}\diff{t}} | Error |
Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]=Divide[Pi,2]*Integrate[Exp[- z*t]*LegendreP[n, 0, 3, t], {t, 1, Infinity}] |
Error | Failure | - | Error |
| 10.54.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = \frac{(-i)^{n+1}}{2\pi}\int_{i\infty}^{(-1+,1+)}e^{izt}\assLegendreQ[]{n}@{t}\diff{t}} | Error |
SphericalBesselJ[n, z]=Divide[(- I)^(n + 1),2*Pi]*Integrate[Exp[I*z*t]*LegendreQ[n, 0, 3, t], {t, I*Infinity, (- 1 + , 1 +)}] |
Error | Failure | - | Error |
| 10.54#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{1}{n}@{z} = \frac{(-i)^{n+1}}{\pi}\int_{i\infty}^{(1+)}e^{izt}\assLegendreQ[]{n}@{t}\diff{t}} | Error |
\|SphericalHankelH2[1, n]* z =Divide[(- I)^(n + 1),Pi]*Integrate[Exp[I*z*t]*LegendreQ[n, 0, 3, t], {t, I*Infinity, (1 +)}] | Error | Failure | - | Error |
| 10.54#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{2}{n}@{z} = \frac{(-i)^{n+1}}{\pi}\int_{i\infty}^{(-1+)}e^{izt}\assLegendreQ[]{n}@{t}\diff{t}} | Error |
\|SphericalHankelH2[2, n]* z =Divide[(- I)^(n + 1),Pi]*Integrate[Exp[I*z*t]*LegendreQ[n, 0, 3, t], {t, I*Infinity, (- 1 +)}] | Error | Failure | - | Error |
| 10.56.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\exp@{-\sqrt{z^{2}+2izt}}}{z} = \frac{e^{-z}}{z}+\frac{2}{\pi}\sum_{n=1}^{\infty}\frac{(-it)^{n}}{n!}\modsphBesselK{n-1}@{z}} | Error |
Divide[Exp[-Sqrt[(z)^(2)+ 2*I*z*t]],z]=Divide[Exp[- z],z]+Divide[2,Pi]*Sum[Divide[(- I*t)^(n),(n)!]*Sqrt[1/2 Pi /z] BesselK[n - 1 + 1/2, z], {n, 1, Infinity}] |
Error | Failure | - | Error |
| 10.57.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}'@{(n+\tfrac{1}{2})z} = \frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{1}{2}}}\BesselJ{n+\frac{1}{2}}'@{(n+\tfrac{1}{2})z}-\frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{3}{2}}}\BesselJ{n+\frac{1}{2}}@{(n+\tfrac{1}{2})z}} | Error |
(D[SphericalBesselJ[n, temp], {temp, 1}]/.temp-> (n +Divide[1,2])* z)=Divide[(Pi)^(Divide[1,2]),((2*n + 1)*z)^(Divide[1,2])]*(D[BesselJ[n +Divide[1,2], temp], {temp, 1}]/.temp-> (n +Divide[1,2])* z)-Divide[(Pi)^(Divide[1,2]),((2*n + 1)*z)^(Divide[3,2])]*BesselJ[n +Divide[1,2], (n +Divide[1,2])* z] |
Error | Failure | - | Successful |
| 10.59.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}e^{ibt}\sphBesselJ{n}@{t}\diff{t} = \begin{cases}\pi i^{n}\assLegendreP[]{n}@{b},&-1} | Error |
Integrate[Exp[I*b*t]*SphericalBesselJ[n, t], {t, - Infinity, Infinity}]= |
Error | Failure | - | - |
| 10.59.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{cases}\pi i^{n}\assLegendreP[]{n}@{b},&-1 < b} | |
|
Error | Failure | - | - |
| 10.59.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b < 1,\\ \frac{1}{2}\pi(+\iunit)^{n},&b} | b < 1 ,(1)/(2)*Pi*(+ I)^(n), |
b < 1 ,Divide[1,2]*Pi*(+ I)^(n), |
Error | Failure | - | Error |
| 10.59.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b < 1,\\ \frac{1}{2}\pi(-\iunit)^{n},&b} | b < 1 ,(1)/(2)*Pi*(- I)^(n), |
b < 1 ,Divide[1,2]*Pi*(- I)^(n), |
Error | Failure | - | Error |
| 10.60.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\cos@@{w}}{w} = -\sum_{n=0}^{\infty}(2n+1)\sphBesselJ{n}@{v}\sphBesselY{n}@{u}\assLegendreP[]{n}@{\cos@@{\alpha}}} | Error |
Divide[Cos[w],w]= - Sum[(2*n + 1)* SphericalBesselJ[n, v]*SphericalBesselY[n, u]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}] |
Error | Failure | - | Error |
| 10.60.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sin@@{w}}{w} = \sum_{n=0}^{\infty}(2n+1)\sphBesselJ{n}@{v}\sphBesselJ{n}@{u}\assLegendreP[]{n}@{\cos@@{\alpha}}} | Error |
Divide[Sin[w],w]= Sum[(2*n + 1)* SphericalBesselJ[n, v]*SphericalBesselJ[n, u]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}] |
Error | Failure | - | Fail
Complex[-0.5468420859284989, -2.0682074571733775] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[1, Times[2, n]], LegendreP[n, Cos[α]], SphericalBesselJ[n, u], SphericalBesselJ[n, v]], {n, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.5468420859284989, 0.7602196675728127] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[1, Times[2, n]], LegendreP[n, Cos[α]], SphericalBesselJ[n, u], SphericalBesselJ[n, v]], {n, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[2.2815850388176915, 0.7602196675728127] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[1, Times[2, n]], LegendreP[n, Cos[α]], SphericalBesselJ[n, u], SphericalBesselJ[n, v]], {n, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.2815850388176915, -2.0682074571733775] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[1, Times[2, n]], LegendreP[n, Cos[α]], SphericalBesselJ[n, u], SphericalBesselJ[n, v]], {n, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.60.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{e^{-w}}{w} = \frac{2}{\pi}\sum_{n=0}^{\infty}(2n+1)\modsphBesseli{1}{n}@{v}\modsphBesselK{n}@{u}\assLegendreP[]{n}@{\cos@@{\alpha}}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* v*Sqrt[1/2 Pi /u] BesselK[n + 1/2, u]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}] | Error | Error | - | - |
| 10.60.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{2z} = -n!z^{n+1}\sum_{k=0}^{n}\frac{2n-2k+1}{k!(2n-k+1)!}\sphBesselJ{n-k}@{z}\sphBesselY{n-k}@{z}} | Error |
SphericalBesselJ[n, 2*z]= - (n)!*(z)^(n + 1)* Sum[Divide[2*n - 2*k + 1,(k)!*(2*n - k + 1)!]*SphericalBesselJ[n - k, z]*SphericalBesselY[n - k, z], {k, 0, n}] |
Error | Failure | - | Skip |
| 10.60.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{n}@{2z} = n!z^{n+1}\sum_{k=0}^{n}\frac{n-k+\frac{1}{2}}{k!(2n-k+1)!}{\left(\sphBesselJ{n-k}^{2}@{z}-\sphBesselY{n-k}^{2}@{z}\right)}} | Error |
SphericalBesselY[n, 2*z]= (n)!*(z)^(n + 1)* Sum[Divide[n - k +Divide[1,2],(k)!*(2*n - k + 1)!]*((SphericalBesselJ[n - k, z])^(2)- (SphericalBesselY[n - k, z])^(2)), {k, 0, n}] |
Error | Failure | - | Error |
| 10.60.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{2z} = \frac{1}{\pi}n!z^{n+1}\sum_{k=0}^{n}(-1)^{k}\frac{2n-2k+1}{k!(2n-k+1)!}\modsphBesselK{n-k}^{2}@{z}} | Error |
Sqrt[1/2 Pi /2*z] BesselK[n + 1/2, 2*z]=Divide[1,Pi]*(n)!*(z)^(n + 1)* Sum[(- 1)^(k)*Divide[2*n - 2*k + 1,(k)!*(2*n - k + 1)!]*(Sqrt[1/2 Pi /z] BesselK[n - k + 1/2, z])^(2), {k, 0, n}] |
Error | Failure | - | Error |
| 10.60.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{iz\cos@@{\alpha}} = \sum_{n=0}^{\infty}(2n+1)i^{n}\sphBesselJ{n}@{z}\assLegendreP[]{n}@{\cos@@{\alpha}}} | Error |
Exp[I*z*Cos[\[Alpha]]]= Sum[(2*n + 1)* (I)^(n)* SphericalBesselJ[n, z]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}] |
Error | Failure | - | Skip |
| 10.60.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{z\cos@@{\alpha}} = \sum_{n=0}^{\infty}(2n+1)\modsphBesseli{1}{n}@{z}\assLegendreP[]{n}@{\cos@@{\alpha}}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}] | Error | Error | - | - |
| 10.60.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-z\cos@@{\alpha}} = \sum_{n=0}^{\infty}(-1)^{n}(2n+1)\modsphBesseli{1}{n}@{z}\assLegendreP[]{n}@{\cos@@{\alpha}}} | Error |
\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]* z*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}] | Error | Error | - | - |
| 10.60.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{0}@{z\sin@@{\alpha}} = \sum_{n=0}^{\infty}(4n+1)\frac{(2n)!}{2^{2n}(n!)^{2}}\sphBesselJ{2n}@{z}\assLegendreP[]{2n}@{\cos@@{\alpha}}} | Error |
BesselJ[0, z*Sin[\[Alpha]]]= Sum[(4*n + 1)*Divide[(2*n)!,(2)^(2*n)*((n)!)^(2)]*SphericalBesselJ[2*n, z]*LegendreP[2*n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}] |
Error | Failure | - | Skip |
| 10.60.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\sphBesselJ{n}^{2}@{z} = \frac{\sinint@{2z}}{2z}} | Error |
Sum[(SphericalBesselJ[n, z])^(2), {n, 0, Infinity}]=Divide[SinIntegral[2*z],2*z] |
Error | Failure | - | Successful |
| 10.60.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}(2n+1)\sphBesselJ{n}^{2}@{z} = 1} | Error |
Sum[(2*n + 1)* (SphericalBesselJ[n, z])^(2), {n, 0, Infinity}]= 1 |
Error | Failure | - | Fail
Complex[0.41421356237309515, 1.4142135623730951] <- {Rule[Sum[Times[Plus[1, Times[2, n]], Power[SphericalBesselJ[n, z], 2]], {n, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.41421356237309515, -1.4142135623730951] <- {Rule[Sum[Times[Plus[1, Times[2, n]], Power[SphericalBesselJ[n, z], 2]], {n, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.414213562373095, -1.4142135623730951] <- {Rule[Sum[Times[Plus[1, Times[2, n]], Power[SphericalBesselJ[n, z], 2]], {n, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.414213562373095, 1.4142135623730951] <- {Rule[Sum[Times[Plus[1, Times[2, n]], Power[SphericalBesselJ[n, z], 2]], {n, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 10.60.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}(-1)^{n}(2n+1)\sphBesselJ{n}^{2}@{z} = \frac{\sin@{2z}}{2z}} | Error |
Sum[(- 1)^(n)*(2*n + 1)* (SphericalBesselJ[n, z])^(2), {n, 0, Infinity}]=Divide[Sin[2*z],2*z] |
Error | Failure | - | Skip |
| 10.60.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}(2n+1)(\sphBesselJ{n}'@{z})^{2} = \tfrac{1}{3}} | Error |
Sum[(2*n + 1)*(((D[SphericalBesselJ[n, temp], {temp, 1}]/.temp-> z)))^(2), {n, 0, Infinity}]=Divide[1,3] |
Error | Failure | - | Error |
| 10.61.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}@@{x}+i\Kelvinbei{\nu}@@{x} = \BesselJ{\nu}@{xe^{3\pi i/4}}} | KelvinBer(nu, x)+ I*KelvinBei(nu, x)= BesselJ(nu, x*exp(3*Pi*I/ 4)) |
KelvinBer[\[Nu], x]+ I*KelvinBei[\[Nu], x]= BesselJ[\[Nu], x*Exp[3*Pi*I/ 4]] |
Successful | Failure | - | Successful |
| 10.61.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{xe^{3\pi i/4}} = e^{\nu\pi i}\BesselJ{\nu}@{xe^{-\pi i/4}}} | BesselJ(nu, x*exp(3*Pi*I/ 4))= exp(nu*Pi*I)*BesselJ(nu, x*exp(- Pi*I/ 4)) |
BesselJ[\[Nu], x*Exp[3*Pi*I/ 4]]= Exp[\[Nu]*Pi*I]*BesselJ[\[Nu], x*Exp[- Pi*I/ 4]] |
Failure | Successful | Successful | - |
| 10.61.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{\nu\pi i}\BesselJ{\nu}@{xe^{-\pi i/4}} = e^{\nu\pi i/2}\modBesselI{\nu}@{xe^{\pi i/4}}} | exp(nu*Pi*I)*BesselJ(nu, x*exp(- Pi*I/ 4))= exp(nu*Pi*I/ 2)*BesselI(nu, x*exp(Pi*I/ 4)) |
Exp[\[Nu]*Pi*I]*BesselJ[\[Nu], x*Exp[- Pi*I/ 4]]= Exp[\[Nu]*Pi*I/ 2]*BesselI[\[Nu], x*Exp[Pi*I/ 4]] |
Failure | Failure | Skip | Successful |
| 10.61.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{\nu\pi i/2}\modBesselI{\nu}@{xe^{\pi i/4}} = e^{3\nu\pi i/2}\modBesselI{\nu}@{xe^{-3\pi i/4}}} | exp(nu*Pi*I/ 2)*BesselI(nu, x*exp(Pi*I/ 4))= exp(3*nu*Pi*I/ 2)*BesselI(nu, x*exp(- 3*Pi*I/ 4)) |
Exp[\[Nu]*Pi*I/ 2]*BesselI[\[Nu], x*Exp[Pi*I/ 4]]= Exp[3*\[Nu]*Pi*I/ 2]*BesselI[\[Nu], x*Exp[- 3*Pi*I/ 4]] |
Failure | Failure | Skip | Successful |
| 10.61.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinker{\nu}@@{x}+i\Kelvinkei{\nu}@@{x} = e^{-\nu\pi i/2}\modBesselK{\nu}@{xe^{\pi i/4}}} | KelvinKer(nu, x)+ I*KelvinKei(nu, x)= exp(- nu*Pi*I/ 2)*BesselK(nu, x*exp(Pi*I/ 4)) |
KelvinKer[\[Nu], x]+ I*KelvinKei[\[Nu], x]= Exp[- \[Nu]*Pi*I/ 2]*BesselK[\[Nu], x*Exp[Pi*I/ 4]] |
Failure | Failure | Successful | Successful |
| 10.61.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\nu\pi i/2}\modBesselK{\nu}@{xe^{\pi i/4}} = \tfrac{1}{2}\pi i\HankelH{1}{\nu}@{xe^{3\pi i/4}}} | exp(- nu*Pi*I/ 2)*BesselK(nu, x*exp(Pi*I/ 4))=(1)/(2)*Pi*I*HankelH1(nu, x*exp(3*Pi*I/ 4)) |
Exp[- \[Nu]*Pi*I/ 2]*BesselK[\[Nu], x*Exp[Pi*I/ 4]]=Divide[1,2]*Pi*I*HankelH1[\[Nu], x*Exp[3*Pi*I/ 4]] |
Failure | Failure | Successful | Successful |
| 10.61.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\pi i\HankelH{1}{\nu}@{xe^{3\pi i/4}} = -\tfrac{1}{2}\pi ie^{-\nu\pi i}\HankelH{2}{\nu}@{xe^{-\pi i/4}}} | (1)/(2)*Pi*I*HankelH1(nu, x*exp(3*Pi*I/ 4))= -(1)/(2)*Pi*I*exp(- nu*Pi*I)*HankelH2(nu, x*exp(- Pi*I/ 4)) |
Divide[1,2]*Pi*I*HankelH1[\[Nu], x*Exp[3*Pi*I/ 4]]= -Divide[1,2]*Pi*I*Exp[- \[Nu]*Pi*I]*HankelH2[\[Nu], x*Exp[- Pi*I/ 4]] |
Failure | Failure | Skip | Successful |
| 10.61.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{2}\deriv[2]{w}{x}+x\deriv{w}{x}-(ix^{2}+\nu^{2})w = 0} | (x)^(2)* diff(w, [x$(2)])+ x*diff(w, x)-(I*(x)^(2)+ (nu)^(2))* w = 0 |
(x)^(2)* D[w, {x, 2}]+ x*D[w, x]-(I*(x)^(2)+ (\[Nu])^(2))* w = 0 |
Failure | Failure | Fail 7.071067807-7.071067807*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), x = 1}11.31370849-11.31370849*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), x = 2}18.38477631-18.38477631*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), x = 3}-7.071067807-7.071067807*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[7.0710678118654755, -7.0710678118654755] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[11.313708498984761, -11.313708498984761] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[18.38477631085024, -18.38477631085024] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.242640687119286, 4.242640687119286] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.61.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{4}\deriv[4]{w}{x}+2x^{3}\deriv[3]{w}{x}-(1+2\nu^{2})\left(x^{2}\deriv[2]{w}{x}-x\deriv{w}{x}\right)+(\nu^{4}-4\nu^{2}+x^{4})w = 0} | (x)^(4)* diff(w, [x$(4)])+ 2*(x)^(3)* diff(w, [x$(3)])-(1 + 2*(nu)^(2))*((x)^(2)* diff(w, [x$(2)])- x*diff(w, x))+((nu)^(4)- 4*(nu)^(2)+ (x)^(4))* w = 0 |
(x)^(4)* D[w, {x, 4}]+ 2*(x)^(3)* D[w, {x, 3}]-(1 + 2*(\[Nu])^(2))*((x)^(2)* D[w, {x, 2}]- x*D[w, x])+((\[Nu])^(4)- 4*(\[Nu])^(2)+ (x)^(4))* w = 0 |
Failure | Failure | Fail 1.414213576-43.84062038*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), x = 1}22.62741701-22.62741695*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), x = 2}114.5512985+69.29646458*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), x = 3}-43.84062038-1.414213576*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[1.4142135623730951, -43.84062043356595] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[22.627416997969522, -22.627416997969522] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[114.5512985522207, 69.29646455628166] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-43.84062043356595, 1.4142135623730951] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 10.61#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{n}@{-x} = (-1)^{n}\Kelvinber{n}@@{x}} | KelvinBer(n, - x)=(- 1)^(n)* KelvinBer(n, x) |
KelvinBer[n, - x]=(- 1)^(n)* KelvinBer[n, x] |
Failure | Failure | Successful | Successful |
| 10.61#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{n}@{-x} = (-1)^{n}\Kelvinbei{n}@@{x}} | KelvinBei(n, - x)=(- 1)^(n)* KelvinBei(n, x) |
KelvinBei[n, - x]=(- 1)^(n)* KelvinBei[n, x] |
Failure | Failure | Successful | Successful |
| 10.61#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{-\nu}@@{x} = \cos@{\nu\pi}\Kelvinber{\nu}@@{x}+\sin@{\nu\pi}\Kelvinbei{\nu}@@{x}+(2/\pi)\sin@{\nu\pi}\Kelvinker{\nu}@@{x}} | KelvinBer(- nu, x)= cos(nu*Pi)*KelvinBer(nu, x)+ sin(nu*Pi)*KelvinBei(nu, x)+(2/ Pi)* sin(nu*Pi)*KelvinKer(nu, x) |
KelvinBer[- \[Nu], x]= Cos[\[Nu]*Pi]*KelvinBer[\[Nu], x]+ Sin[\[Nu]*Pi]*KelvinBei[\[Nu], x]+(2/ Pi)* Sin[\[Nu]*Pi]*KelvinKer[\[Nu], x] |
Failure | Failure | Successful | Successful |
| 10.61#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{-\nu}@@{x} = -\sin@{\nu\pi}\Kelvinber{\nu}@@{x}+\cos@{\nu\pi}\Kelvinbei{\nu}@@{x}+(2/\pi)\sin@{\nu\pi}\Kelvinkei{\nu}@@{x}} | KelvinBei(- nu, x)= - sin(nu*Pi)*KelvinBer(nu, x)+ cos(nu*Pi)*KelvinBei(nu, x)+(2/ Pi)* sin(nu*Pi)*KelvinKei(nu, x) |
KelvinBei[- \[Nu], x]= - Sin[\[Nu]*Pi]*KelvinBer[\[Nu], x]+ Cos[\[Nu]*Pi]*KelvinBei[\[Nu], x]+(2/ Pi)* Sin[\[Nu]*Pi]*KelvinKei[\[Nu], x] |
Failure | Failure | Successful | Successful |
| 10.61#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinker{-\nu}@@{x} = \cos@{\nu\pi}\Kelvinker{\nu}@@{x}-\sin@{\nu\pi}\Kelvinkei{\nu}@@{x}} | KelvinKer(- nu, x)= cos(nu*Pi)*KelvinKer(nu, x)- sin(nu*Pi)*KelvinKei(nu, x) |
KelvinKer[- \[Nu], x]= Cos[\[Nu]*Pi]*KelvinKer[\[Nu], x]- Sin[\[Nu]*Pi]*KelvinKei[\[Nu], x] |
Failure | Failure | Successful | Successful |
| 10.61#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinkei{-\nu}@@{x} = \sin@{\nu\pi}\Kelvinker{\nu}@@{x}+\cos@{\nu\pi}\Kelvinkei{\nu}@@{x}} | KelvinKei(- nu, x)= sin(nu*Pi)*KelvinKer(nu, x)+ cos(nu*Pi)*KelvinKei(nu, x) |
KelvinKei[- \[Nu], x]= Sin[\[Nu]*Pi]*KelvinKer[\[Nu], x]+ Cos[\[Nu]*Pi]*KelvinKei[\[Nu], x] |
Failure | Failure | Successful | Successful |
| 10.61#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{-n}@@{x} = (-1)^{n}\Kelvinber{n}@@{x},~{}\Kelvinbei{-n}@@{x}} | KelvinBer(- n, x)=(- 1)^(n)* KelvinBer(n, x),*KelvinBei(- n, x) |
KelvinBer[- n, x]=(- 1)^(n)* KelvinBer[n, x],*KelvinBei[- n, x] |
Error | Failure | - | Error |
| 10.61#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (-1)^{n}\Kelvinber{n}@@{x},~{}\Kelvinbei{-n}@@{x} = (-1)^{n}\Kelvinbei{n}@@{x}} | (- 1)^(n)* KelvinBer(n, x),*KelvinBei(- n, x)=(- 1)^(n)* KelvinBei(n, x) |
(- 1)^(n)* KelvinBer[n, x],*KelvinBei[- n, x]=(- 1)^(n)* KelvinBei[n, x] |
Error | Failure | - | Error |
| 10.61#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinker{-n}@@{x} = (-1)^{n}\Kelvinker{n}@@{x},~{}\Kelvinkei{-n}@@{x}} | KelvinKer(- n, x)=(- 1)^(n)* KelvinKer(n, x),*KelvinKei(- n, x) |
KelvinKer[- n, x]=(- 1)^(n)* KelvinKer[n, x],*KelvinKei[- n, x] |
Error | Failure | - | Error |
| 10.61#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (-1)^{n}\Kelvinker{n}@@{x},~{}\Kelvinkei{-n}@@{x} = (-1)^{n}\Kelvinkei{n}@@{x}} | (- 1)^(n)* KelvinKer(n, x),*KelvinKei(- n, x)=(- 1)^(n)* KelvinKei(n, x) |
(- 1)^(n)* KelvinKer[n, x],*KelvinKei[- n, x]=(- 1)^(n)* KelvinKei[n, x] |
Error | Failure | - | Error |
| 10.61#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\frac{1}{2}}@{x\sqrt{2}} = \frac{2^{-\frac{3}{4}}}{\sqrt{\pi x}}\left(e^{x}\cos@{x+\frac{\pi}{8}}-e^{-x}\cos@{x-\frac{\pi}{8}}\right)} | KelvinBer((1)/(2), x*sqrt(2))=((2)^(-(3)/(4)))/(sqrt(Pi*x))*(exp(x)*cos(x +(Pi)/(8))- exp(- x)*cos(x -(Pi)/(8))) |
KelvinBer[Divide[1,2], x*Sqrt[2]]=Divide[(2)^(-Divide[3,4]),Sqrt[Pi*x]]*(Exp[x]*Cos[x +Divide[Pi,8]]- Exp[- x]*Cos[x -Divide[Pi,8]]) |
Failure | Failure | Successful | Successful |
| 10.61#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{\frac{1}{2}}@{x\sqrt{2}} = \frac{2^{-\frac{3}{4}}}{\sqrt{\pi x}}\left(e^{x}\sin@{x+\frac{\pi}{8}}+\,e^{-x}\sin@{x-\frac{\pi}{8}}\right)} | KelvinBei((1)/(2), x*sqrt(2))=((2)^(-(3)/(4)))/(sqrt(Pi*x))*(exp(x)*sin(x +(Pi)/(8))+ exp(- x)*sin(x -(Pi)/(8))) |
KelvinBei[Divide[1,2], x*Sqrt[2]]=Divide[(2)^(-Divide[3,4]),Sqrt[Pi*x]]*(Exp[x]*Sin[x +Divide[Pi,8]]+ Exp[- x]*Sin[x -Divide[Pi,8]]) |
Failure | Failure | Successful | Successful |
| 10.61#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{-\frac{1}{2}}@{x\sqrt{2}} = \frac{2^{-\frac{3}{4}}}{\sqrt{\pi x}}\left(e^{x}\sin@{x+\frac{\pi}{8}}-e^{-x}\sin@{x-\frac{\pi}{8}}\right)} | KelvinBer(-(1)/(2), x*sqrt(2))=((2)^(-(3)/(4)))/(sqrt(Pi*x))*(exp(x)*sin(x +(Pi)/(8))- exp(- x)*sin(x -(Pi)/(8))) |
KelvinBer[-Divide[1,2], x*Sqrt[2]]=Divide[(2)^(-Divide[3,4]),Sqrt[Pi*x]]*(Exp[x]*Sin[x +Divide[Pi,8]]- Exp[- x]*Sin[x -Divide[Pi,8]]) |
Failure | Failure | Successful | Successful |
| 10.61#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{-\frac{1}{2}}@{x\sqrt{2}} = -\frac{2^{-\frac{3}{4}}}{\sqrt{\pi x}}\left(e^{x}\cos@{x+\frac{\pi}{8}}+e^{-x}\cos@{x-\frac{\pi}{8}}\right)} | KelvinBei(-(1)/(2), x*sqrt(2))= -((2)^(-(3)/(4)))/(sqrt(Pi*x))*(exp(x)*cos(x +(Pi)/(8))+ exp(- x)*cos(x -(Pi)/(8))) |
KelvinBei[-Divide[1,2], x*Sqrt[2]]= -Divide[(2)^(-Divide[3,4]),Sqrt[Pi*x]]*(Exp[x]*Cos[x +Divide[Pi,8]]+ Exp[- x]*Cos[x -Divide[Pi,8]]) |
Failure | Failure | Successful | Successful |
| 10.61.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinker{\frac{1}{2}}@{x\sqrt{2}} = \Kelvinkei{-\frac{1}{2}}@{x\sqrt{2}}} | KelvinKer((1)/(2), x*sqrt(2))= KelvinKei(-(1)/(2), x*sqrt(2)) |
KelvinKer[Divide[1,2], x*Sqrt[2]]= KelvinKei[-Divide[1,2], x*Sqrt[2]] |
Successful | Failure | - | Successful |
| 10.61.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinkei{-\frac{1}{2}}@{x\sqrt{2}} = -2^{-\frac{3}{4}}\sqrt{\frac{\pi}{x}}e^{-x}\sin@{x-\frac{\pi}{8}}} | KelvinKei(-(1)/(2), x*sqrt(2))= - (2)^(-(3)/(4))*sqrt((Pi)/(x))*exp(- x)*sin(x -(Pi)/(8)) |
KelvinKei[-Divide[1,2], x*Sqrt[2]]= - (2)^(-Divide[3,4])*Sqrt[Divide[Pi,x]]*Exp[- x]*Sin[x -Divide[Pi,8]] |
Failure | Failure | Successful | Successful |
| 10.61.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinkei{\frac{1}{2}}@{x\sqrt{2}} = -\Kelvinker{-\frac{1}{2}}@{x\sqrt{2}}} | KelvinKei((1)/(2), x*sqrt(2))= - KelvinKer(-(1)/(2), x*sqrt(2)) |
KelvinKei[Divide[1,2], x*Sqrt[2]]= - KelvinKer[-Divide[1,2], x*Sqrt[2]] |
Successful | Successful | - | - |
| 10.61.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\Kelvinker{-\frac{1}{2}}@{x\sqrt{2}} = -2^{-\frac{3}{4}}\sqrt{\frac{\pi}{x}}e^{-x}\cos@{x-\frac{\pi}{8}}} | - KelvinKer(-(1)/(2), x*sqrt(2))= - (2)^(-(3)/(4))*sqrt((Pi)/(x))*exp(- x)*cos(x -(Pi)/(8)) |
- KelvinKer[-Divide[1,2], x*Sqrt[2]]= - (2)^(-Divide[3,4])*Sqrt[Divide[Pi,x]]*Exp[- x]*Cos[x -Divide[Pi,8]] |
Failure | Successful | Successful | - |
| 10.63#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2}\Kelvinber{}'@@{x} = \Kelvinber{1}@@{x}+\Kelvinbei{1}@@{x}} | subs( temp=x, diff( KelvinBer(, temp), temp$(1) ) )= KelvinBer(1, x)+ KelvinBei(1, x) |
(D[KelvinBer[, temp], {temp, 1}]/.temp-> x)= KelvinBer[1, x]+ KelvinBei[1, x] |
Error | Successful | - | - |
| 10.63#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2}\Kelvinbei{}'@@{x} = -\Kelvinber{1}x+\Kelvinbei{1}x} | subs( temp=x, diff( KelvinBei(, temp), temp$(1) ) )= - KelvinBer(1, x)+ KelvinBei(1, x) |
(D[KelvinBei[, temp], {temp, 1}]/.temp-> x)= - KelvinBer[1, x]+ KelvinBei[1, x] |
Error | Successful | - | - |
| 10.63#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2}\Kelvinker{}'@@{x} = \Kelvinker{1}x+\Kelvinkei{1}x} | subs( temp=x, diff( KelvinKer(, temp), temp$(1) ) )= KelvinKer(1, x)+ KelvinKei(1, x) |
(D[KelvinKer[, temp], {temp, 1}]/.temp-> x)= KelvinKer[1, x]+ KelvinKei[1, x] |
Error | Failure | - | Fail
Complex[-1.1863575732592084, 14.181995430502623] <- {Rule[Null, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[2.2791430867712648, 1.1716762871697879] <- {Rule[Null, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[0.6426179371583077, -0.28537763977623365] <- {Rule[Null, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[-1.186357573259207, -14.181995430502624] <- {Rule[Null, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}... skip entries to safe data |
| 10.63#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2}\Kelvinkei{}'@@{x} = -\Kelvinker{1}x+\Kelvinkei{1}x} | subs( temp=x, diff( KelvinKei(, temp), temp$(1) ) )= - KelvinKer(1, x)+ KelvinKei(1, x) |
(D[KelvinKei[, temp], {temp, 1}]/.temp-> x)= - KelvinKer[1, x]+ KelvinKei[1, x] |
Error | Successful | - | - |
| 10.63#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{\nu} = \Kelvinber{\nu}^{2}@@{x}+\Kelvinbei{\nu}^{2}@@{x}} | p[nu]= (KelvinBer(nu, x))^(2)+ (KelvinBei(nu, x))^(2) |
Subscript[p, \[Nu]]= (KelvinBer[\[Nu], x])^(2)+ (KelvinBei[\[Nu], x])^(2) |
Failure | Failure | Fail 1.558095916+1.23230553*I <- {nu = 2^(1/2)+I*2^(1/2), p[nu] = 2^(1/2)+I*2^(1/2), x = 1}2.2705317+2.829827546*I <- {nu = 2^(1/2)+I*2^(1/2), p[nu] = 2^(1/2)+I*2^(1/2), x = 2}-.9860947+6.1991516*I <- {nu = 2^(1/2)+I*2^(1/2), p[nu] = 2^(1/2)+I*2^(1/2), x = 3}1.558095916-1.59612159*I <- {nu = 2^(1/2)+I*2^(1/2), p[nu] = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Successful |
| 10.63#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{\nu} = \Kelvinber{\nu}@@{x}\Kelvinbei{\nu}'@@{x}-\Kelvinber{\nu}'@@{x}\Kelvinbei{\nu}@@{x}} | q[nu]= KelvinBer(nu, x)*subs( temp=x, diff( KelvinBei(nu, temp), temp$(1) ) )- subs( temp=x, diff( KelvinBer(nu, temp), temp$(1) ) )*KelvinBei(nu, x) |
Subscript[q, \[Nu]]= KelvinBer[\[Nu], x]*(D[KelvinBei[\[Nu], temp], {temp, 1}]/.temp-> x)- (D[KelvinBer[\[Nu], temp], {temp, 1}]/.temp-> x)*KelvinBei[\[Nu], x] |
Failure | Failure | Fail 1.42000721+1.37316601*I <- {nu = 2^(1/2)+I*2^(1/2), q[nu] = 2^(1/2)+I*2^(1/2), x = 1}1.93113589+1.7044153*I <- {nu = 2^(1/2)+I*2^(1/2), q[nu] = 2^(1/2)+I*2^(1/2), x = 2}1.38678669+4.3022397*I <- {nu = 2^(1/2)+I*2^(1/2), q[nu] = 2^(1/2)+I*2^(1/2), x = 3}1.42000721-1.45526111*I <- {nu = 2^(1/2)+I*2^(1/2), q[nu] = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Successful |
| 10.63#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r_{\nu} = \Kelvinber{\nu}@@{x}\Kelvinber{\nu}'@@{x}+\Kelvinbei{\nu}@@{x}\Kelvinbei{\nu}'@@{x}} | r[nu]= KelvinBer(nu, x)*subs( temp=x, diff( KelvinBer(nu, temp), temp$(1) ) )+ KelvinBei(nu, x)*subs( temp=x, diff( KelvinBei(nu, temp), temp$(1) ) ) |
Subscript[r, \[Nu]]= KelvinBer[\[Nu], x]*(D[KelvinBer[\[Nu], temp], {temp, 1}]/.temp-> x)+ KelvinBei[\[Nu], x]*(D[KelvinBei[\[Nu], temp], {temp, 1}]/.temp-> x) |
Failure | Failure | Fail 1.87424466+1.35972583*I <- {nu = 2^(1/2)+I*2^(1/2), r[nu] = 2^(1/2)+I*2^(1/2), x = 1}1.0714855+2.99841206*I <- {nu = 2^(1/2)+I*2^(1/2), r[nu] = 2^(1/2)+I*2^(1/2), x = 2}-1.5010775+2.94632015*I <- {nu = 2^(1/2)+I*2^(1/2), r[nu] = 2^(1/2)+I*2^(1/2), x = 3}1.87424466-1.46870129*I <- {nu = 2^(1/2)+I*2^(1/2), r[nu] = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Successful |
| 10.63#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{\nu} = \left(\Kelvinber{\nu}'@@{x}\right)^{2}+\left(\Kelvinbei{\nu}'@@{x}\right)^{2}} | s[nu]=(subs( temp=x, diff( KelvinBer(nu, temp), temp$(1) ) ))^(2)+(subs( temp=x, diff( KelvinBei(nu, temp), temp$(1) ) ))^(2) |
Subscript[s, \[Nu]]=(((D[KelvinBer[\[Nu], temp], {temp, 1}]/.temp-> x)))^(2)+(((D[KelvinBei[\[Nu], temp], {temp, 1}]/.temp-> x)))^(2) |
Failure | Failure | Fail 2.1390486+1.97888025*I <- {nu = 2^(1/2)+I*2^(1/2), s[nu] = 2^(1/2)+I*2^(1/2), x = 1}.31664947+2.31090336*I <- {nu = 2^(1/2)+I*2^(1/2), s[nu] = 2^(1/2)+I*2^(1/2), x = 2}.7948503e-1+2.54111021*I <- {nu = 2^(1/2)+I*2^(1/2), s[nu] = 2^(1/2)+I*2^(1/2), x = 3}2.1390486-.849546872*I <- {nu = 2^(1/2)+I*2^(1/2), s[nu] = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Successful |
| 10.64.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\cos@{x\sin@@{t}-nt}\cosh@{x\sin@@{t}}\diff{t}} | KelvinBer(n, x*sqrt(2))=((- 1)^(n))/(Pi)*int(cos(x*sin(t)- n*t)*cosh(x*sin(t)), t = 0..Pi) |
KelvinBer[n, x*Sqrt[2]]=Divide[(- 1)^(n),Pi]*Integrate[Cos[x*Sin[t]- n*t]*Cosh[x*Sin[t]], {t, 0, Pi}] |
Failure | Failure | Skip | Error |
| 10.64.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\sin@{x\sin@@{t}-nt}\sinh@{x\sin@@{t}}\diff{t}} | KelvinBei(n, x*sqrt(2))=((- 1)^(n))/(Pi)*int(sin(x*sin(t)- n*t)*sinh(x*sin(t)), t = 0..Pi) |
KelvinBei[n, x*Sqrt[2]]=Divide[(- 1)^(n),Pi]*Integrate[Sin[x*Sin[t]- n*t]*Sinh[x*Sin[t]], {t, 0, Pi}] |
Failure | Failure | Skip | Error |
| 10.65#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}@@{x} = (\tfrac{1}{2}x)^{\nu}\sum_{k=0}^{\infty}\frac{\cos@{\frac{3}{4}\nu\pi+\frac{1}{2}k\pi}}{k!\EulerGamma@{\nu+k+1}}(\tfrac{1}{4}x^{2})^{k}} | KelvinBer(nu, x)=((1)/(2)*x)^(nu)* sum((cos((3)/(4)*nu*Pi +(1)/(2)*k*Pi))/(factorial(k)*GAMMA(nu + k + 1))*((1)/(4)*(x)^(2))^(k), k = 0..infinity) |
KelvinBer[\[Nu], x]=(Divide[1,2]*x)^(\[Nu])* Sum[Divide[Cos[Divide[3,4]*\[Nu]*Pi +Divide[1,2]*k*Pi],(k)!*Gamma[\[Nu]+ k + 1]]*(Divide[1,4]*(x)^(2))^(k), {k, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 10.65#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{\nu}@@{x} = (\tfrac{1}{2}x)^{\nu}\sum_{k=0}^{\infty}\frac{\sin@{\frac{3}{4}\nu\pi+\frac{1}{2}k\pi}}{k!\EulerGamma@{\nu+k+1}}(\tfrac{1}{4}x^{2})^{k}} | KelvinBei(nu, x)=((1)/(2)*x)^(nu)* sum((sin((3)/(4)*nu*Pi +(1)/(2)*k*Pi))/(factorial(k)*GAMMA(nu + k + 1))*((1)/(4)*(x)^(2))^(k), k = 0..infinity) |
KelvinBei[\[Nu], x]=(Divide[1,2]*x)^(\[Nu])* Sum[Divide[Sin[Divide[3,4]*\[Nu]*Pi +Divide[1,2]*k*Pi],(k)!*Gamma[\[Nu]+ k + 1]]*(Divide[1,4]*(x)^(2))^(k), {k, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 10.65#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinker{}@@{x} = -\ln@{\tfrac{1}{2}x}\Kelvinber{}@@{x}+\tfrac{1}{4}\pi\Kelvinbei{}@@{x}+\sum_{k=0}^{\infty}(-1)^{k}\frac{\digamma@{2k+1}}{((2k)!)^{2}}(\tfrac{1}{4}x^{2})^{2k}} | KelvinBei(, x)+ sum((- 1)^(k)*(Psi(2*k + 1))/((factorial(2*k))^(2))*((1)/(4)*(x)^(2))^(2*k), k = 0..infinity) |
KelvinBei[, x]+ Sum[(- 1)^(k)*Divide[PolyGamma[2*k + 1],((2*k)!)^(2)]*(Divide[1,4]*(x)^(2))^(2*k), {k, 0, Infinity}] |
Error | Failure | - | Error |
| 10.65#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinkei{}@@{x} = -\ln@{\tfrac{1}{2}x}\Kelvinbei{}@@{x}-\tfrac{1}{4}\pi\Kelvinber{}@@{x}+\sum_{k=0}^{\infty}(-1)^{k}\frac{\digamma@{2k+2}}{((2k+1)!)^{2}}(\tfrac{1}{4}x^{2})^{2k+1}} | KelvinBer(, x)+ sum((- 1)^(k)*(Psi(2*k + 2))/((factorial(2*k + 1))^(2))*((1)/(4)*(x)^(2))^(2*k + 1), k = 0..infinity) |
KelvinBer[, x]+ Sum[(- 1)^(k)*Divide[PolyGamma[2*k + 2],((2*k + 1)!)^(2)]*(Divide[1,4]*(x)^(2))^(2*k + 1), {k, 0, Infinity}] |
Error | Failure | - | Fail
Complex[-9.498271428543017, -1.4209618670710054] <- {Rule[Null, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[0.18667337329748546, -13.49491576100636] <- {Rule[Null, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[2.6690254116240313, -21.496718507485472] <- {Rule[Null, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[-9.498271428543028, 1.4209618670710045] <- {Rule[Null, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}... skip entries to safe data |
| 10.65.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}^{2}@@{x}+\Kelvinbei{\nu}^{2}@@{x} = (\tfrac{1}{2}x)^{2\nu}\sum_{k=0}^{\infty}\frac{1}{\EulerGamma@{\nu+k+1}\EulerGamma@{\nu+2k+1}}\frac{(\frac{1}{4}x^{2})^{2k}}{k!}} | (KelvinBer(nu, x))^(2)+ (KelvinBei(nu, x))^(2)=((1)/(2)*x)^(2*nu)* sum((1)/(GAMMA(nu + k + 1)*GAMMA(nu + 2*k + 1))*(((1)/(4)*(x)^(2))^(2*k))/(factorial(k)), k = 0..infinity) |
(KelvinBer[\[Nu], x])^(2)+ (KelvinBei[\[Nu], x])^(2)=(Divide[1,2]*x)^(2*\[Nu])* Sum[Divide[1,Gamma[\[Nu]+ k + 1]*Gamma[\[Nu]+ 2*k + 1]]*Divide[(Divide[1,4]*(x)^(2))^(2*k),(k)!], {k, 0, Infinity}] |
Successful | Failure | - | Successful |
| 10.65.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}@@{x}\Kelvinbei{\nu}'@@{x}-\Kelvinber{\nu}'@@{x}\Kelvinbei{\nu}@@{x} = (\tfrac{1}{2}x)^{2\nu+1}\sum_{k=0}^{\infty}\frac{1}{\EulerGamma@{\nu+k+1}\EulerGamma@{\nu+2k+2}}\frac{(\frac{1}{4}x^{2})^{2k}}{k!}} | KelvinBer(nu, x)*subs( temp=x, diff( KelvinBei(nu, temp), temp$(1) ) )- subs( temp=x, diff( KelvinBer(nu, temp), temp$(1) ) )*KelvinBei(nu, x)=((1)/(2)*x)^(2*nu + 1)* sum((1)/(GAMMA(nu + k + 1)*GAMMA(nu + 2*k + 2))*(((1)/(4)*(x)^(2))^(2*k))/(factorial(k)), k = 0..infinity) |
KelvinBer[\[Nu], x]*(D[KelvinBei[\[Nu], temp], {temp, 1}]/.temp-> x)- (D[KelvinBer[\[Nu], temp], {temp, 1}]/.temp-> x)*KelvinBei[\[Nu], x]=(Divide[1,2]*x)^(2*\[Nu]+ 1)* Sum[Divide[1,Gamma[\[Nu]+ k + 1]*Gamma[\[Nu]+ 2*k + 2]]*Divide[(Divide[1,4]*(x)^(2))^(2*k),(k)!], {k, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 10.65.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}@@{x}\Kelvinber{\nu}'@@{x}+\Kelvinbei{\nu}@@{x}\Kelvinbei{\nu}'@@{x} = \tfrac{1}{2}(\tfrac{1}{2}x)^{2\nu-1}\sum_{k=0}^{\infty}\frac{1}{\EulerGamma@{\nu+k+1}\EulerGamma@{\nu+2k}}\frac{(\frac{1}{4}x^{2})^{2k}}{k!}} | KelvinBer(nu, x)*subs( temp=x, diff( KelvinBer(nu, temp), temp$(1) ) )+ KelvinBei(nu, x)*subs( temp=x, diff( KelvinBei(nu, temp), temp$(1) ) )=(1)/(2)*((1)/(2)*x)^(2*nu - 1)* sum((1)/(GAMMA(nu + k + 1)*GAMMA(nu + 2*k))*(((1)/(4)*(x)^(2))^(2*k))/(factorial(k)), k = 0..infinity) |
KelvinBer[\[Nu], x]*(D[KelvinBer[\[Nu], temp], {temp, 1}]/.temp-> x)+ KelvinBei[\[Nu], x]*(D[KelvinBei[\[Nu], temp], {temp, 1}]/.temp-> x)=Divide[1,2]*(Divide[1,2]*x)^(2*\[Nu]- 1)* Sum[Divide[1,Gamma[\[Nu]+ k + 1]*Gamma[\[Nu]+ 2*k]]*Divide[(Divide[1,4]*(x)^(2))^(2*k),(k)!], {k, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 10.65.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\Kelvinber{\nu}'@@{x}\right)^{2}+\left(\Kelvinbei{\nu}'@@{x}\right)^{2} = (\tfrac{1}{2}x)^{2\nu-2}\sum_{k=0}^{\infty}\frac{2k^{2}+2\nu k+\frac{1}{4}\nu^{2}}{\EulerGamma@{\nu+k+1}\EulerGamma@{\nu+2k+1}}\frac{(\frac{1}{4}x^{2})^{2k}}{k!}} | (subs( temp=x, diff( KelvinBer(nu, temp), temp$(1) ) ))^(2)+(subs( temp=x, diff( KelvinBei(nu, temp), temp$(1) ) ))^(2)=((1)/(2)*x)^(2*nu - 2)* sum((2*(k)^(2)+ 2*nu*k +(1)/(4)*(nu)^(2))/(GAMMA(nu + k + 1)*GAMMA(nu + 2*k + 1))*(((1)/(4)*(x)^(2))^(2*k))/(factorial(k)), k = 0..infinity) |
(((D[KelvinBer[\[Nu], temp], {temp, 1}]/.temp-> x)))^(2)+(((D[KelvinBei[\[Nu], temp], {temp, 1}]/.temp-> x)))^(2)=(Divide[1,2]*x)^(2*\[Nu]- 2)* Sum[Divide[2*(k)^(2)+ 2*\[Nu]*k +Divide[1,4]*(\[Nu])^(2),Gamma[\[Nu]+ k + 1]*Gamma[\[Nu]+ 2*k + 1]]*Divide[(Divide[1,4]*(x)^(2))^(2*k),(k)!], {k, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 10.66.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}@@{x}+i\Kelvinbei{\nu}@@{x} = \sum_{k=0}^{\infty}\frac{e^{(3\nu+k)\pi i/4}x^{k}\BesselJ{\nu+k}@{x}}{2^{k/2}k!}} | KelvinBer(nu, x)+ I*KelvinBei(nu, x)= sum((exp((3*nu + k)* Pi*I/ 4)*(x)^(k)* BesselJ(nu + k, x))/((2)^(k/ 2)* factorial(k)), k = 0..infinity) |
KelvinBer[\[Nu], x]+ I*KelvinBei[\[Nu], x]= Sum[Divide[Exp[(3*\[Nu]+ k)* Pi*I/ 4]*(x)^(k)* BesselJ[\[Nu]+ k, x],(2)^(k/ 2)* (k)!], {k, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 10.66.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=0}^{\infty}\frac{e^{(3\nu+k)\pi i/4}x^{k}\BesselJ{\nu+k}@{x}}{2^{k/2}k!} = \sum_{k=0}^{\infty}\frac{e^{(3\nu+3k)\pi i/4}x^{k}\modBesselI{\nu+k}@{x}}{2^{k/2}k!}} | sum((exp((3*nu + k)* Pi*I/ 4)*(x)^(k)* BesselJ(nu + k, x))/((2)^(k/ 2)* factorial(k)), k = 0..infinity)= sum((exp((3*nu + 3*k)* Pi*I/ 4)*(x)^(k)* BesselI(nu + k, x))/((2)^(k/ 2)* factorial(k)), k = 0..infinity) |
Sum[Divide[Exp[(3*\[Nu]+ k)* Pi*I/ 4]*(x)^(k)* BesselJ[\[Nu]+ k, x],(2)^(k/ 2)* (k)!], {k, 0, Infinity}]= Sum[Divide[Exp[(3*\[Nu]+ 3*k)* Pi*I/ 4]*(x)^(k)* BesselI[\[Nu]+ k, x],(2)^(k/ 2)* (k)!], {k, 0, Infinity}] |
Failure | Successful | Skip | - |
| 10.66#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{n}@{x\sqrt{2}} = \sum_{k=-\infty}^{\infty}(-1)^{n+k}\BesselJ{n+2k}@{x}\modBesselI{2k}@{x}} | KelvinBer(n, x*sqrt(2))= sum((- 1)^(n + k)* BesselJ(n + 2*k, x)*BesselI(2*k, x), k = - infinity..infinity) |
KelvinBer[n, x*Sqrt[2]]= Sum[(- 1)^(n + k)* BesselJ[n + 2*k, x]*BesselI[2*k, x], {k, - Infinity, Infinity}] |
Failure | Successful | Skip | - |
| 10.66#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{n}@{x\sqrt{2}} = \sum_{k=-\infty}^{\infty}(-1)^{n+k}\BesselJ{n+2k+1}@{x}\modBesselI{2k+1}@{x}} | KelvinBei(n, x*sqrt(2))= sum((- 1)^(n + k)* BesselJ(n + 2*k + 1, x)*BesselI(2*k + 1, x), k = - infinity..infinity) |
KelvinBei[n, x*Sqrt[2]]= Sum[(- 1)^(n + k)* BesselJ[n + 2*k + 1, x]*BesselI[2*k + 1, x], {k, - Infinity, Infinity}] |
Failure | Successful | Skip | - |
| 10.71.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int x^{1+\nu}f_{\nu}\diff{x} = -\frac{x^{1+\nu}}{\sqrt{2}}(f_{\nu+1}-g_{\nu+1})} | int((x)^(1 + nu)* f[nu], x)= -((x)^(1 + nu))/(sqrt(2))*(f[nu + 1]- g[nu + 1]) |
Integrate[(x)^(1 + \[Nu])* Subscript[f, \[Nu]], x]= -Divide[(x)^(1 + \[Nu]),Sqrt[2]]*(Subscript[f, \[Nu]+ 1]- Subscript[g, \[Nu]+ 1]) |
Failure | Failure | Skip | Successful |
| 10.71.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int x^{1-\nu}f_{\nu}\diff{x} = \frac{x^{1-\nu}}{\sqrt{2}}(f_{\nu-1}-g_{\nu-1})} | int((x)^(1 - nu)* f[nu], x)=((x)^(1 - nu))/(sqrt(2))*(f[nu - 1]- g[nu - 1]) |
Integrate[(x)^(1 - \[Nu])* Subscript[f, \[Nu]], x]=Divide[(x)^(1 - \[Nu]),Sqrt[2]]*(Subscript[f, \[Nu]- 1]- Subscript[g, \[Nu]- 1]) |
Failure | Failure | Skip | Successful |
| 10.71.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int xf_{\nu}g_{\nu}\diff{x} = \tfrac{1}{4}x^{2}\left(2f_{\nu}g_{\nu}-f_{\nu-1}g_{\nu+1}-f_{\nu+1}g_{\nu-1}\right)} | int(x*f[nu]*g[nu], x)=(1)/(4)*(x)^(2)*(2*f[nu]*g[nu]- f[nu - 1]*g[nu + 1]- f[nu + 1]*g[nu - 1]) |
Integrate[x*Subscript[f, \[Nu]]*Subscript[g, \[Nu]], x]=Divide[1,4]*(x)^(2)*(2*Subscript[f, \[Nu]]*Subscript[g, \[Nu]]- Subscript[f, \[Nu]- 1]*Subscript[g, \[Nu]+ 1]- Subscript[f, \[Nu]+ 1]*Subscript[g, \[Nu]- 1]) |
Failure | Failure | Skip | Skip |
| 10.71.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int x(f_{\nu}^{2}-g_{\nu}^{2})\diff{x} = \tfrac{1}{2}x^{2}\left(f_{\nu}^{2}-f_{\nu-1}f_{\nu+1}-g_{\nu}^{2}+g_{\nu-1}g_{\nu+1}\right)} | int(x*(f(f[nu])^(2)- g(g[nu])^(2)), x)=(f(f[nu])^(2)- f[nu - 1]*f[nu + 1]- g(g[nu])^(2)+ g[nu - 1]*g[nu + 1]) |
Integrate[x*(f(Subscript[f, \[Nu]])^(2)- g(Subscript[g, \[Nu]])^(2)), x]=(f(Subscript[f, \[Nu]])^(2)- Subscript[f, \[Nu]- 1]*Subscript[f, \[Nu]+ 1]- g(Subscript[g, \[Nu]])^(2)+ Subscript[g, \[Nu]- 1]*Subscript[g, \[Nu]+ 1]) |
Failure | Failure | Skip | Successful |
| 10.73.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{r}\pderiv{}{r}\left(r\pderiv{V}{r}\right)+\frac{1}{r^{2}}\pderiv[2]{V}{\phi}+\pderiv[2]{V}{z} = 0} | (1)/(r)*diff((r*diff(V, r))+(1)/((r)^(2))*diff(V, [phi$(2)]), r)+ diff(V, [z$(2)])= 0 |
Divide[1,r]*D[(r*D[V, r])+Divide[1,(r)^(2)]*D[V, {\[Phi], 2}], r]+ D[V, {z, 2}]= 0 |
Successful | Failure | - | Successful |