Results of Struve and Related Functions
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| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 11.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{\nu}@{z} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(-1)^{n}(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}} | StruveH(nu, z)=((1)/(2)*z)^(nu + 1)* sum(((- 1)^(n)*((1)/(2)*z)^(2*n))/(GAMMA(n +(3)/(2))*GAMMA(n + nu +(3)/(2))), n = 0..infinity) |
StruveH[\[Nu], z]=(Divide[1,2]*z)^(\[Nu]+ 1)* Sum[Divide[(- 1)^(n)*(Divide[1,2]*z)^(2*n),Gamma[n +Divide[3,2]]*Gamma[n + \[Nu]+Divide[3,2]]], {n, 0, Infinity}] |
Successful | Successful | - | - |
| 11.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modStruveL{\nu}@{z} = -ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz}} | StruveL(nu, z)= - I*exp(-(1)/(2)*Pi*I*nu)*StruveH(nu, I*z) |
StruveL[\[Nu], z]= - I*Exp[-Divide[1,2]*Pi*I*\[Nu]]*StruveH[\[Nu], I*z] |
Failure | Failure | Fail -.9119368045e-1-212.1906008*I <- {nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}23.48378801+14.39748233*I <- {nu = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-183.2849891-97.24822718*I <- {nu = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}746.7960427+104.9552444*I <- {nu = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-0.09119395476353123, -212.19060110903138] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[23.48378803135987, 14.397482376436031] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-183.28498965036638, -97.24822703421293] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[746.7960436976847, 104.95524615581924] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 11.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}} | - I*exp(-(1)/(2)*Pi*I*nu)*StruveH(nu, I*z)=((1)/(2)*z)^(nu + 1)* sum((((1)/(2)*z)^(2*n))/(GAMMA(n +(3)/(2))*GAMMA(n + nu +(3)/(2))), n = 0..infinity) |
- I*Exp[-Divide[1,2]*Pi*I*\[Nu]]*StruveH[\[Nu], I*z]=(Divide[1,2]*z)^(\[Nu]+ 1)* Sum[Divide[(Divide[1,2]*z)^(2*n),Gamma[n +Divide[3,2]]*Gamma[n + \[Nu]+Divide[3,2]]], {n, 0, Infinity}] |
Failure | Failure | Skip | Fail
Complex[0.09119395476353123, 212.19060110903138] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-23.48378803135987, -14.397482376436031] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[183.28498965036638, 97.24822703421293] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-746.7960436976847, -104.95524615581924] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 11.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveK{\nu}@{z} = \StruveH{\nu}@{z}-\BesselY{\nu}@{z}} | StruveH(nu, z) - BesselY(nu, z)= StruveH(nu, z)- BesselY(nu, z) |
StruveH[\[Nu], z] - BesselY[\[Nu], z]= StruveH[\[Nu], z]- BesselY[\[Nu], z] |
Successful | Successful | - | - |
| 11.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modStruveM{\nu}@{z} = \modStruveL{\nu}@{z}-\modBesselI{\nu}@{z}} | StruveL(nu, z) - BesselI(nu, z)= StruveL(nu, z)- BesselI(nu, z) |
StruveL[\[Nu], z] - BesselI[\[Nu], z]= StruveL[\[Nu], z]- BesselI[\[Nu], z] |
Successful | Successful | - | - |
| 11.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}+\left(1-\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}} | diff(w, [z$(2)])+(1)/(z)*diff(w, z)+(1 -((nu)^(2))/((z)^(2)))* w =(((1)/(2)*z)^(nu - 1))/(sqrt(Pi)*GAMMA(nu +(1)/(2))) |
D[w, {z, 2}]+Divide[1,z]*D[w, z]+(1 -Divide[(\[Nu])^(2),(z)^(2)])* w =Divide[(Divide[1,2]*z)^(\[Nu]- 1),Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]] |
Failure | Failure | Fail -.3292528958+.1261718930*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)}1.117431897+5.592974705*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)}2.886594176+29.83865170*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)}2.791726027+2.817686588*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[-0.3292528958392771, 0.1261718930121784] <- {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[1.1174318983838325, 0.0638795414755875] <- {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[-9.829307268242317, -7.250178123857234] <- {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[3.2003851737933693, 1.557087772272263] <- {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 |
| 11.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \StruveH{\nu}@{z},\StruveK{\nu}@{z}} | w = StruveH(nu, z), StruveH(nu, z) - BesselY(nu, z) |
w = StruveH[\[Nu], z], StruveH[\[Nu], z] - BesselY[\[Nu], z] |
Error | Failure | - | Error |
| 11.2.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}-\left(1+\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}} | diff(w, [z$(2)])+(1)/(z)*diff(w, z)-(1 +((nu)^(2))/((z)^(2)))* w =(((1)/(2)*z)^(nu - 1))/(sqrt(Pi)*GAMMA(nu +(1)/(2))) |
D[w, {z, 2}]+Divide[1,z]*D[w, z]-(1 +Divide[(\[Nu])^(2),(z)^(2)])* w =Divide[(Divide[1,2]*z)^(\[Nu]- 1),Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]] |
Failure | Failure | Fail -3.157680020-2.702255231*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)}-1.710995227+2.764547581*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)}.58167052e-1+27.01022458*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)}-.3670109651e-1-.1074053566e-1*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[-3.1576800205854676, -2.702255231734012] <- {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[-1.7109952263623578, -2.764547583270603] <- {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[-12.657734392988507, -10.078605248603424] <- {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[0.3719580490471791, -1.2713393524739274] <- {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 |
| 11.2.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \modStruveL{\nu}@{z},\modStruveM{\nu}@{z}} | w = StruveL(nu, z), StruveL(nu, z) - BesselI(nu, z) |
w = StruveL[\[Nu], z], StruveL[\[Nu], z] - BesselI[\[Nu], z] |
Error | Failure | - | Error |
| 11.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \StruveH{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}} | w = StruveH(nu, x)+ A*BesselJ(nu, x)+ B*BesselY(nu, x) |
w = StruveH[\[Nu], x]+ A*BesselJ[\[Nu], x]+ B*BesselY[\[Nu], x] |
Failure | Failure | Fail 1.813177648+3.357588143*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), w = 2^(1/2)+I*2^(1/2), x = 1}-.3533489224+4.243660941*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), w = 2^(1/2)+I*2^(1/2), x = 2}-3.044392825+1.991205432*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), w = 2^(1/2)+I*2^(1/2), x = 3}1.813177648+.5291610183*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), w = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Skip |
| 11.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \StruveK{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}} | w = StruveH(nu, x) - BesselY(nu, x)+ A*BesselJ(nu, x)+ B*BesselY(nu, x) |
w = StruveH[\[Nu], x] - BesselY[\[Nu], x]+ A*BesselJ[\[Nu], x]+ B*BesselY[\[Nu], x] |
Failure | Failure | Fail 1.240425455+3.227234897*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), w = 2^(1/2)+I*2^(1/2), x = 1}-1.194165497+3.657602257*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), w = 2^(1/2)+I*2^(1/2), x = 2}-3.012593980+.934563193*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), w = 2^(1/2)+I*2^(1/2), x = 3}1.240425455+.3988077733*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), w = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Skip |
| 11.2.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{1}{\nu}@{z}} | w = StruveH(nu, z)+ A*BesselJ(nu, z)+ B*HankelH1(nu, z) |
w = StruveH[\[Nu], z]+ A*BesselJ[\[Nu], z]+ B*HankelH1[\[Nu], z] |
Failure | Failure | Skip | Skip |
| 11.2.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{2}{\nu}@{z}} | w = StruveH(nu, z)+ A*BesselJ(nu, z)+ B*HankelH2(nu, z) |
w = StruveH[\[Nu], z]+ A*BesselJ[\[Nu], z]+ B*HankelH2[\[Nu], z] |
Failure | Failure | Skip | Skip |
| 11.2.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \StruveK{\nu}@{z}+A\HankelH{1}{\nu}@{z}+B\HankelH{2}{\nu}@{z}} | w = StruveH(nu, z) - BesselY(nu, z)+ A*HankelH1(nu, z)+ B*HankelH2(nu, z) |
w = StruveH[\[Nu], z] - BesselY[\[Nu], z]+ A*HankelH1[\[Nu], z]+ B*HankelH2[\[Nu], z] |
Failure | Failure | Skip | Skip |
| 11.2.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \modStruveL{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}} | w = StruveL(nu, z)+ A*BesselK(nu, z)+ B*BesselI(nu, z) |
w = StruveL[\[Nu], z]+ A*BesselK[\[Nu], z]+ B*BesselI[\[Nu], z] |
Failure | Failure | Skip | Skip |
| 11.2.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \modStruveM{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}} | w = StruveL(nu, z) - BesselI(nu, z)+ A*BesselK(nu, z)+ B*BesselI(nu, z) |
w = StruveL[\[Nu], z] - BesselI[\[Nu], z]+ A*BesselK[\[Nu], z]+ B*BesselI[\[Nu], z] |
Failure | Failure | Skip | Skip |
| 11.4.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveK{n+\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sum_{m=0}^{n}\frac{(2m)!\,2^{-2m}}{m!\,(n-m)!}\,(\tfrac{1}{2}z)^{n-2m}} | StruveH(n +(1)/(2), z) - BesselY(n +(1)/(2), z)=((2)/(Pi*z))^((1)/(2))* sum((factorial(2*m)*(2)^(- 2*m))/(factorial(m)*factorial(n - m))*((1)/(2)*z)^(n - 2*m), m = 0..n) |
StruveH[n +Divide[1,2], z] - BesselY[n +Divide[1,2], z]=(Divide[2,Pi*z])^(Divide[1,2])* Sum[Divide[(2*m)!*(2)^(- 2*m),(m)!*(n - m)!]*(Divide[1,2]*z)^(n - 2*m), {m, 0, n}] |
Failure | Failure | Skip | Successful |
| 11.4.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modStruveL{n+\frac{1}{2}}@{z} = \modBesselI{-n-\frac{1}{2}}@{z}-\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sum_{m=0}^{n}\frac{(-1)^{m}(2m)!\,2^{-2m}}{m!\,(n-m)!}\,(\tfrac{1}{2}z)^{n-2m}} | StruveL(n +(1)/(2), z)= BesselI(- n -(1)/(2), z)-((2)/(Pi*z))^((1)/(2))* sum(((- 1)^(m)*factorial(2*m)*(2)^(- 2*m))/(factorial(m)*factorial(n - m))*((1)/(2)*z)^(n - 2*m), m = 0..n) |
StruveL[n +Divide[1,2], z]= BesselI[- n -Divide[1,2], z]-(Divide[2,Pi*z])^(Divide[1,2])* Sum[Divide[(- 1)^(m)*(2*m)!*(2)^(- 2*m),(m)!*(n - m)!]*(Divide[1,2]*z)^(n - 2*m), {m, 0, n}] |
Failure | Failure | Skip | Successful |
| 11.4.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{-n-\frac{1}{2}}@{z} = (-1)^{n}\BesselJ{n+\frac{1}{2}}@{z}} | StruveH(- n -(1)/(2), z)=(- 1)^(n)* BesselJ(n +(1)/(2), z) |
StruveH[- n -Divide[1,2], z]=(- 1)^(n)* BesselJ[n +Divide[1,2], z] |
Failure | Failure | Successful | Successful |
| 11.4.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modStruveL{-n-\frac{1}{2}}@{z} = \modBesselI{n+\frac{1}{2}}@{z}} | StruveL(- n -(1)/(2), z)= BesselI(n +(1)/(2), z) |
StruveL[- n -Divide[1,2], z]= BesselI[n +Divide[1,2], z] |
Failure | Failure | Successful | Successful |
| 11.4.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}(1-\cos@@{z})} | StruveH((1)/(2), z)=((2)/(Pi*z))^((1)/(2))*(1 - cos(z)) |
StruveH[Divide[1,2], z]=(Divide[2,Pi*z])^(Divide[1,2])*(1 - Cos[z]) |
Failure | Failure | Successful | Successful |
| 11.4.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{-\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sin@@{z}} | StruveH(-(1)/(2), z)=((2)/(Pi*z))^((1)/(2))* sin(z) |
StruveH[-Divide[1,2], z]=(Divide[2,Pi*z])^(Divide[1,2])* Sin[z] |
Failure | Failure | Successful | Successful |
| 11.4.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modStruveL{\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}(\cosh@@{z}-1)} | StruveL((1)/(2), z)=((2)/(Pi*z))^((1)/(2))*(cosh(z)- 1) |
StruveL[Divide[1,2], z]=(Divide[2,Pi*z])^(Divide[1,2])*(Cosh[z]- 1) |
Failure | Failure | Successful | Successful |
| 11.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modStruveL{-\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sinh@@{z}} | StruveL(-(1)/(2), z)=((2)/(Pi*z))^((1)/(2))* sinh(z) |
StruveL[-Divide[1,2], z]=(Divide[2,Pi*z])^(Divide[1,2])* Sinh[z] |
Failure | Failure | Successful | Successful |
| 11.4.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{\frac{3}{2}}@{z} = \left(\frac{z}{2\pi}\right)^{\frac{1}{2}}\left(1+\frac{2}{z^{2}}\right)-\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\left(\sin@@{z}+\frac{\cos@@{z}}{z}\right)} | StruveH((3)/(2), z)=((z)/(2*Pi))^((1)/(2))*(1 +(2)/((z)^(2)))-((2)/(Pi*z))^((1)/(2))*(sin(z)+(cos(z))/(z)) |
StruveH[Divide[3,2], z]=(Divide[z,2*Pi])^(Divide[1,2])*(1 +Divide[2,(z)^(2)])-(Divide[2,Pi*z])^(Divide[1,2])*(Sin[z]+Divide[Cos[z],z]) |
Failure | Failure | Successful | Successful |
| 11.4.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{-\frac{3}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\left(\cos@@{z}-\frac{\sin@@{z}}{z}\right)} | StruveH(-(3)/(2), z)=((2)/(Pi*z))^((1)/(2))*(cos(z)-(sin(z))/(z)) |
StruveH[-Divide[3,2], z]=(Divide[2,Pi*z])^(Divide[1,2])*(Cos[z]-Divide[Sin[z],z]) |
Failure | Failure | Successful | Successful |
| 11.4.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modStruveL{\frac{3}{2}}@{z} = -\left(\frac{z}{2\pi}\right)^{\frac{1}{2}}\left(1-\frac{2}{z^{2}}\right)+\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\left(\sinh@@{z}-\frac{\cosh@@{z}}{z}\right)} | StruveL((3)/(2), z)= -((z)/(2*Pi))^((1)/(2))*(1 -(2)/((z)^(2)))+((2)/(Pi*z))^((1)/(2))*(sinh(z)-(cosh(z))/(z)) |
StruveL[Divide[3,2], z]= -(Divide[z,2*Pi])^(Divide[1,2])*(1 -Divide[2,(z)^(2)])+(Divide[2,Pi*z])^(Divide[1,2])*(Sinh[z]-Divide[Cosh[z],z]) |
Failure | Failure | Successful | Successful |
| 11.4.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modStruveL{-\frac{3}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\left(\cosh@@{z}-\frac{\sinh@@{z}}{z}\right)} | StruveL(-(3)/(2), z)=((2)/(Pi*z))^((1)/(2))*(cosh(z)-(sinh(z))/(z)) |
StruveL[-Divide[3,2], z]=(Divide[2,Pi*z])^(Divide[1,2])*(Cosh[z]-Divide[Sinh[z],z]) |
Failure | Failure | Successful | Successful |
| 11.4.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{\nu}@{x} >= 0} | StruveH(nu, x)> = 0 |
StruveH[\[Nu], x]> = 0 |
Failure | Failure | Skip | Successful |
| 11.4.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu+1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}(1+\vartheta)} | StruveH(nu, z)=(2*((1)/(2)*z)^(nu + 1))/(sqrt(Pi)*GAMMA(nu +(3)/(2)))*(1 + vartheta) |
StruveH[\[Nu], z]=Divide[2*(Divide[1,2]*z)^(\[Nu]+ 1),Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]*(1 + \[CurlyTheta]) |
Failure | Failure | Fail -.1259323815-.6376916086*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2)}-.5771716954+.6854347047e-1*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)-I*2^(1/2)}.1290633837+.5197827843*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), vartheta = -2^(1/2)-I*2^(1/2)}.5803026975-.1864522947*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), vartheta = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Skip |
| 11.4.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\vartheta| < \frac{2}{3}\exp@{\frac{\tfrac{1}{4}|z|^{2}}{|\nu_{0}+\tfrac{3}{2}|}-1}} | abs(vartheta)<(2)/(3)*exp(((1)/(4)*(abs(z))^(2))/(abs(nu[0]+(3)/(2)))- 1) |
Abs[\[CurlyTheta]]<Divide[2,3]*Exp[Divide[Divide[1,4]*(Abs[z])^(2),Abs[Subscript[\[Nu], 0]+Divide[3,2]]]- 1] |
Failure | Failure | Fail 2. < .3339546072 <- {z = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), nu[0] = 2^(1/2)+I*2^(1/2)}2. < .3339546072 <- {z = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), nu[0] = 2^(1/2)-I*2^(1/2)}2. < .4967563064 <- {z = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), nu[0] = -2^(1/2)-I*2^(1/2)}2. < .4967563064 <- {z = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), nu[0] = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Skip |
| 11.4.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{\nu}@{ze^{m\pi i}} = e^{m\pi i(\nu+1)}\StruveH{\nu}@{z}} | StruveH(nu, z*exp(m*Pi*I))= exp(m*Pi*I*(nu + 1))*StruveH(nu, z) |
StruveH[\[Nu], z*Exp[m*Pi*I]]= Exp[m*Pi*I*(\[Nu]+ 1)]*StruveH[\[Nu], z] |
Failure | Failure | Fail 13.93052781-18.31382455*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}-.5904691739e-2-.3463835767e-1*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 3}.2512942813+.1005768782*I <- {nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), m = 3}-2.971927621-.3003885072*I <- {nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), m = 3}... skip entries to safe data |
Error |
| 11.4.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modStruveL{\nu}@{ze^{m\pi i}} = e^{m\pi i(\nu+1)}\modStruveL{\nu}@{z}} | StruveL(nu, z*exp(m*Pi*I))= exp(m*Pi*I*(nu + 1))*StruveL(nu, z) |
StruveL[\[Nu], z*Exp[m*Pi*I]]= Exp[m*Pi*I*(\[Nu]+ 1)]*StruveL[\[Nu], z] |
Failure | Failure | Fail 23.48202217-14.39410521*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}-.1507858067e-1-.2518674877e-1*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 3}.2367740036+.2211567113*I <- {nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), m = 3}-2.405166395+.6652992785*I <- {nu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), m = 3}... skip entries to safe data |
Error |
| 11.4.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{\nu}@{z} = \frac{4}{\pi^{1/2}\EulerGamma@{\nu+\tfrac{1}{2}}}\*\sum_{k=0}^{\infty}\frac{(2k+\nu+1)\EulerGamma@{k+\nu+1}}{k!(2k+1)(2k+2\nu+1)}\BesselJ{2k+\nu+1}@{z}} | StruveH(nu, z)=(4)/((Pi)^(1/ 2)* GAMMA(nu +(1)/(2)))* sum(((2*k + nu + 1)* GAMMA(k + nu + 1))/(factorial(k)*(2*k + 1)*(2*k + 2*nu + 1))*BesselJ(2*k + nu + 1, z), k = 0..infinity) |
StruveH[\[Nu], z]=Divide[4,(Pi)^(1/ 2)* Gamma[\[Nu]+Divide[1,2]]]* Sum[Divide[(2*k + \[Nu]+ 1)* Gamma[k + \[Nu]+ 1],(k)!*(2*k + 1)*(2*k + 2*\[Nu]+ 1)]*BesselJ[2*k + \[Nu]+ 1, z], {k, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 11.4.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{\nu}@{z} = \left(\frac{z}{2\pi}\right)^{1/2}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{2}z)^{k}}{k!(k+\tfrac{1}{2})}\BesselJ{k+\nu+\frac{1}{2}}@{z}} | StruveH(nu, z)=((z)/(2*Pi))^(1/ 2)* sum((((1)/(2)*z)^(k))/(factorial(k)*(k +(1)/(2)))*BesselJ(k + nu +(1)/(2), z), k = 0..infinity) |
StruveH[\[Nu], z]=(Divide[z,2*Pi])^(1/ 2)* Sum[Divide[(Divide[1,2]*z)^(k),(k)!*(k +Divide[1,2])]*BesselJ[k + \[Nu]+Divide[1,2], z], {k, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 11.4.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu+\frac{1}{2}}}{\EulerGamma@{\nu+\tfrac{1}{2}}}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{2}z)^{k}}{k!(k+\nu+\tfrac{1}{2})}\BesselJ{k+\frac{1}{2}}@{z}} | StruveH(nu, z)=(((1)/(2)*z)^(nu +(1)/(2)))/(GAMMA(nu +(1)/(2)))*sum((((1)/(2)*z)^(k))/(factorial(k)*(k + nu +(1)/(2)))*BesselJ(k +(1)/(2), z), k = 0..infinity) |
StruveH[\[Nu], z]=Divide[(Divide[1,2]*z)^(\[Nu]+Divide[1,2]),Gamma[\[Nu]+Divide[1,2]]]*Sum[Divide[(Divide[1,2]*z)^(k),(k)!*(k + \[Nu]+Divide[1,2])]*BesselJ[k +Divide[1,2], z], {k, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 11.4.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{0}@{z} = \frac{4}{\pi}\sum_{k=0}^{\infty}\frac{\BesselJ{2k+1}@{z}}{2k+1}} | StruveH(0, z)=(4)/(Pi)*sum((BesselJ(2*k + 1, z))/(2*k + 1), k = 0..infinity) |
StruveH[0, z]=Divide[4,Pi]*Sum[Divide[BesselJ[2*k + 1, z],2*k + 1], {k, 0, Infinity}] |
Failure | Successful | Skip | - |
| 11.4.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{4}{\pi}\sum_{k=0}^{\infty}\frac{\BesselJ{2k+1}@{z}}{2k+1} = 2\sum_{k=0}^{\infty}(-1)^{k}\BesselJ{k+\frac{1}{2}}^{2}@{\tfrac{1}{2}z}} | (4)/(Pi)*sum((BesselJ(2*k + 1, z))/(2*k + 1), k = 0..infinity)= 2*sum((- 1)^(k)* (BesselJ(k +(1)/(2), (1)/(2)*z))^(2), k = 0..infinity) |
Divide[4,Pi]*Sum[Divide[BesselJ[2*k + 1, z],2*k + 1], {k, 0, Infinity}]= 2*Sum[(- 1)^(k)* (BesselJ[k +Divide[1,2], Divide[1,2]*z])^(2), {k, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 11.4.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{1}@{z} = \frac{2}{\pi}(1-\BesselJ{0}@{z})+\frac{4}{\pi}\sum_{k=1}^{\infty}\frac{\BesselJ{2k}@{z}}{4k^{2}-1}} | StruveH(1, z)=(2)/(Pi)*(1 - BesselJ(0, z))+(4)/(Pi)*sum((BesselJ(2*k, z))/(4*(k)^(2)- 1), k = 1..infinity) |
StruveH[1, z]=Divide[2,Pi]*(1 - BesselJ[0, z])+Divide[4,Pi]*Sum[Divide[BesselJ[2*k, z],4*(k)^(2)- 1], {k, 1, Infinity}] |
Failure | Successful | Skip | - |
| 11.4.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}(1-\BesselJ{0}@{z})+\frac{4}{\pi}\sum_{k=1}^{\infty}\frac{\BesselJ{2k}@{z}}{4k^{2}-1} = 4\sum_{k=0}^{\infty}\BesselJ{2k+\frac{1}{2}}@{\tfrac{1}{2}z}\BesselJ{2k+\frac{3}{2}}@{\tfrac{1}{2}z}} | (2)/(Pi)*(1 - BesselJ(0, z))+(4)/(Pi)*sum((BesselJ(2*k, z))/(4*(k)^(2)- 1), k = 1..infinity)= 4*sum(BesselJ(2*k +(1)/(2), (1)/(2)*z)*BesselJ(2*k +(3)/(2), (1)/(2)*z), k = 0..infinity) |
Divide[2,Pi]*(1 - BesselJ[0, z])+Divide[4,Pi]*Sum[Divide[BesselJ[2*k, z],4*(k)^(2)- 1], {k, 1, Infinity}]= 4*Sum[BesselJ[2*k +Divide[1,2], Divide[1,2]*z]*BesselJ[2*k +Divide[3,2], Divide[1,2]*z], {k, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 11.4.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{\nu-1}@{z}+\StruveH{\nu+1}@{z} = \frac{2\nu}{z}\StruveH{\nu}@{z}+\frac{(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}} | StruveH(nu - 1, z)+ StruveH(nu + 1, z)=(2*nu)/(z)*StruveH(nu, z)+(((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(3)/(2))) |
StruveH[\[Nu]- 1, z]+ StruveH[\[Nu]+ 1, z]=Divide[2*\[Nu],z]*StruveH[\[Nu], z]+Divide[(Divide[1,2]*z)^(\[Nu]),Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]] |
Failure | Successful | Successful | - |
| 11.4.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{\nu-1}@{z}-\StruveH{\nu+1}@{z} = 2\!\StruveH{\nu}'@{z}-\frac{(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}} | StruveH(nu - 1, z)- StruveH(nu + 1, z)= 2*subs( temp=z, diff( StruveH(nu, temp), temp$(1) ) )-(((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(3)/(2))) |
StruveH[\[Nu]- 1, z]- StruveH[\[Nu]+ 1, z]= 2*(D[StruveH[\[Nu], temp], {temp, 1}]/.temp-> z)-Divide[(Divide[1,2]*z)^(\[Nu]),Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]] |
Failure | Successful | Successful | - |
| 11.4.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modStruveL{\nu-1}@{z}-\modStruveL{\nu+1}@{z} = \frac{2\nu}{z}\modStruveL{\nu}@{z}+\frac{(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}} | StruveL(nu - 1, z)- StruveL(nu + 1, z)=(2*nu)/(z)*StruveL(nu, z)+(((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(3)/(2))) |
StruveL[\[Nu]- 1, z]- StruveL[\[Nu]+ 1, z]=Divide[2*\[Nu],z]*StruveL[\[Nu], z]+Divide[(Divide[1,2]*z)^(\[Nu]),Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]] |
Failure | Successful | Successful | - |
| 11.4.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modStruveL{\nu-1}@{z}+\modStruveL{\nu+1}@{z} = 2\!\modStruveL{\nu}'@{z}-\frac{(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}} | StruveL(nu - 1, z)+ StruveL(nu + 1, z)= 2*subs( temp=z, diff( StruveL(nu, temp), temp$(1) ) )-(((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(3)/(2))) |
StruveL[\[Nu]- 1, z]+ StruveL[\[Nu]+ 1, z]= 2*(D[StruveL[\[Nu], temp], {temp, 1}]/.temp-> z)-Divide[(Divide[1,2]*z)^(\[Nu]),Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]] |
Failure | Successful | Successful | - |
| 11.4.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\left(z^{\nu}\StruveH{\nu}@{z}\right) = z^{\nu}\StruveH{\nu-1}@{z}} | diff((z)^(nu)* StruveH(nu, z), z)= (z)^(nu)* StruveH(nu - 1, z) |
D[(z)^(\[Nu])* StruveH[\[Nu], z], z]= (z)^(\[Nu])* StruveH[\[Nu]- 1, z] |
Failure | Successful | Successful | - |
| 11.4.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\left(z^{-\nu}\StruveH{\nu}@{z}\right) = \frac{2^{-\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}-z^{-\nu}\StruveH{\nu+1}@{z}} | diff((z)^(- nu)* StruveH(nu, z), z)=((2)^(- nu))/(sqrt(Pi)*GAMMA(nu +(3)/(2)))- (z)^(- nu)* StruveH(nu + 1, z) |
D[(z)^(- \[Nu])* StruveH[\[Nu], z], z]=Divide[(2)^(- \[Nu]),Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]- (z)^(- \[Nu])* StruveH[\[Nu]+ 1, z] |
Successful | Successful | - | - |
| 11.4.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\left(z^{\nu}\modStruveL{\nu}@{z}\right) = z^{\nu}\modStruveL{\nu-1}@{z}} | diff((z)^(nu)* StruveL(nu, z), z)= (z)^(nu)* StruveL(nu - 1, z) |
D[(z)^(\[Nu])* StruveL[\[Nu], z], z]= (z)^(\[Nu])* StruveL[\[Nu]- 1, z] |
Failure | Successful | Successful | - |
| 11.4.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\left(z^{-\nu}\modStruveL{\nu}@{z}\right) = \frac{2^{-\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}+z^{-\nu}\modStruveL{\nu+1}@{z}} | diff((z)^(- nu)* StruveL(nu, z), z)=((2)^(- nu))/(sqrt(Pi)*GAMMA(nu +(3)/(2)))+ (z)^(- nu)* StruveL(nu + 1, z) |
D[(z)^(- \[Nu])* StruveL[\[Nu], z], z]=Divide[(2)^(- \[Nu]),Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]+ (z)^(- \[Nu])* StruveL[\[Nu]+ 1, z] |
Successful | Successful | - | - |
| 11.4#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{0}'@{z} = \frac{2}{\pi}-\StruveH{1}@{z}} | subs( temp=z, diff( StruveH(0, temp), temp$(1) ) )=(2)/(Pi)- StruveH(1, z) |
(D[StruveH[0, temp], {temp, 1}]/.temp-> z)=Divide[2,Pi]- StruveH[1, z] |
Successful | Successful | - | - |
| 11.4#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}(z\StruveH{1}@{z}) = z\StruveH{0}@{z}} | diff(z*StruveH(1, z), z)= z*StruveH(0, z) |
D[z*StruveH[1, z], z]= z*StruveH[0, z] |
Successful | Successful | - | - |
| 11.4#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modStruveL{0}'@{z} = \frac{2}{\pi}+\modStruveL{1}@{z}} | subs( temp=z, diff( StruveL(0, temp), temp$(1) ) )=(2)/(Pi)+ StruveL(1, z) |
(D[StruveL[0, temp], {temp, 1}]/.temp-> z)=Divide[2,Pi]+ StruveL[1, z] |
Successful | Successful | - | - |
| 11.4#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}(z\modStruveL{1}@{z}) = z\modStruveL{0}@{z}} | diff(z*StruveL(1, z), z)= z*StruveL(0, z) |
D[z*StruveL[1, z], z]= z*StruveL[0, z] |
Successful | Successful | - | - |
| 11.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveH{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{1}(1-t^{2})^{\nu-\frac{1}{2}}\sin@{zt}\diff{t}} | StruveH(nu, z)=(2*((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* sin(z*t), t = 0..1) |
StruveH[\[Nu], z]=Divide[2*(Divide[1,2]*z)^(\[Nu]),Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Sin[z*t], {t, 0, 1}] |
Successful | Successful | - | - |
| 11.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{1}(1-t^{2})^{\nu-\frac{1}{2}}\sin@{zt}\diff{t} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\pi/2}\sin@{z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}} | (2*((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* sin(z*t), t = 0..1)=(2*((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))*int(sin(z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi/ 2) |
Divide[2*(Divide[1,2]*z)^(\[Nu]),Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Sin[z*t], {t, 0, 1}]=Divide[2*(Divide[1,2]*z)^(\[Nu]),Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]*Integrate[Sin[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi/ 2}] |
Successful | Successful | - | - |
| 11.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveK{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\infty}e^{-zt}(1+t^{2})^{\nu-\frac{1}{2}}\diff{t}} | StruveH(nu, z) - BesselY(nu, z)=(2*((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))*int(exp(- z*t)*(1 + (t)^(2))^(nu -(1)/(2)), t = 0..infinity) |
StruveH[\[Nu], z] - BesselY[\[Nu], z]=Divide[2*(Divide[1,2]*z)^(\[Nu]),Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*t]*(1 + (t)^(2))^(\[Nu]-Divide[1,2]), {t, 0, Infinity}] |
Successful | Failure | - | Error |
| 11.5.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \StruveK{0}@{z} = \frac{2}{\pi}\int_{0}^{\infty}e^{-z\sinh@@{t}}\diff{t}} | StruveH(0, z) - BesselY(0, z)=(2)/(Pi)*int(exp(- z*sinh(t)), t = 0..infinity) |
StruveH[0, z] - BesselY[0, z]=Divide[2,Pi]*Integrate[Exp[- z*Sinh[t]], {t, 0, Infinity}] |
Successful | Failure | - | Error |
| 11.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modStruveM{\nu}@{z} = -\frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{1}e^{-zt}(1-t^{2})^{\nu-\frac{1}{2}}\diff{t}} | StruveL(nu, z) - BesselI(nu, z)= -(2*((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))*int(exp(- z*t)*(1 - (t)^(2))^(nu -(1)/(2)), t = 0..1) |
StruveL[\[Nu], z] - BesselI[\[Nu], z]= -Divide[2*(Divide[1,2]*z)^(\[Nu]),Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*t]*(1 - (t)^(2))^(\[Nu]-Divide[1,2]), {t, 0, 1}] |
Successful | Successful | - | - |
| 11.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modStruveM{0}@{z} = -\frac{2}{\pi}\int_{0}^{\pi/2}e^{-z\cos@@{\theta}}\diff{\theta}} | StruveL(0, z) - BesselI(0, z)= -(2)/(Pi)*int(exp(- z*cos(theta)), theta = 0..Pi/ 2) |
StruveL[0, z] - BesselI[0, z]= -Divide[2,Pi]*Integrate[Exp[- z*Cos[\[Theta]]], {\[Theta], 0, Pi/ 2}] |
Successful | Successful | - | - |
| 11.5.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modStruveL{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\pi/2}\sinh@{z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}} | StruveL(nu, z)=(2*((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))*int(sinh(z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi/ 2) |
StruveL[\[Nu], z]=Divide[2*(Divide[1,2]*z)^(\[Nu]),Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]*Integrate[Sinh[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi/ 2}] |
Successful | Failure | - | Error |
| 11.5.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{-\nu}@{x}-\modStruveL{\nu}@{x} = \frac{2(\tfrac{1}{2}x)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\infty}(1+t^{2})^{\nu-\frac{1}{2}}\sin@{xt}\diff{t}} | BesselI(- nu, x)- StruveL(nu, x)=(2*((1)/(2)*x)^(nu))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))*int((1 + (t)^(2))^(nu -(1)/(2))* sin(x*t), t = 0..infinity) |
BesselI[- \[Nu], x]- StruveL[\[Nu], x]=Divide[2*(Divide[1,2]*x)^(\[Nu]),Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 + (t)^(2))^(\[Nu]-Divide[1,2])* Sin[x*t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 11.5.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\tfrac{1}{2}x)^{-\nu-1}\StruveH{\nu}@{x} = -\frac{1}{2\pi i}\int_{-i\infty}^{i\infty}\frac{\pi\csc@{\pi s}}{\EulerGamma@{\tfrac{3}{2}+s}\EulerGamma@{\tfrac{3}{2}+\nu+s}}(\tfrac{1}{4}x^{2})^{s}\diff{s}} | ((1)/(2)*x)^(- nu - 1)* StruveH(nu, x)= -(1)/(2*Pi*I)*int((Pi*csc(Pi*s))/(GAMMA((3)/(2)+ s)*GAMMA((3)/(2)+ nu + s))*((1)/(4)*(x)^(2))^(s), s = - I*infinity..I*infinity) |
(Divide[1,2]*x)^(- \[Nu]- 1)* StruveH[\[Nu], x]= -Divide[1,2*Pi*I]*Integrate[Divide[Pi*Csc[Pi*s],Gamma[Divide[3,2]+ s]*Gamma[Divide[3,2]+ \[Nu]+ s]]*(Divide[1,4]*(x)^(2))^(s), {s, - I*Infinity, I*Infinity}] |
Failure | Failure | Skip | Error |
| 11.5.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\tfrac{1}{2}z)^{-\nu-1}\modStruveL{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty}^{(0+)}\frac{\pi\csc@{\pi s}}{\EulerGamma@{\tfrac{3}{2}+s}\EulerGamma@{\tfrac{3}{2}+\nu+s}}(-\tfrac{1}{4}z^{2})^{s}\diff{s}} | ((1)/(2)*z)^(- nu - 1)* StruveL(nu, z)=(1)/(2*Pi*I)*int((Pi*csc(Pi*s))/(GAMMA((3)/(2)+ s)*GAMMA((3)/(2)+ nu + s))*(-(1)/(4)*(z)^(2))^(s), s = infinity..(0 +)) |
(Divide[1,2]*z)^(- \[Nu]- 1)* StruveL[\[Nu], z]=Divide[1,2*Pi*I]*Integrate[Divide[Pi*Csc[Pi*s],Gamma[Divide[3,2]+ s]*Gamma[Divide[3,2]+ \[Nu]+ s]]*(-Divide[1,4]*(z)^(2))^(s), {s, Infinity, (0 +)}] |
Error | Failure | - | Error |
| 11.7.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int z^{\nu}\StruveH{\nu-1}@{z}\diff{z} = z^{\nu}\StruveH{\nu}@{z}} | int((z)^(nu)* StruveH(nu - 1, z), z)= (z)^(nu)* StruveH(nu, z) |
Integrate[(z)^(\[Nu])* StruveH[\[Nu]- 1, z], z]= (z)^(\[Nu])* StruveH[\[Nu], z] |
Successful | Successful | - | - |
| 11.7.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int z^{-\nu}\StruveH{\nu+1}@{z}\diff{z} = -z^{-\nu}\StruveH{\nu}@{z}+\frac{2^{-\nu}z}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}} | int((z)^(- nu)* StruveH(nu + 1, z), z)= - (z)^(- nu)* StruveH(nu, z)+((2)^(- nu)* z)/(sqrt(Pi)*GAMMA(nu +(3)/(2))) |
Integrate[(z)^(- \[Nu])* StruveH[\[Nu]+ 1, z], z]= - (z)^(- \[Nu])* StruveH[\[Nu], z]+Divide[(2)^(- \[Nu])* z,Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]] |
Successful | Successful | - | - |
| 11.7.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int z^{\nu}\modStruveL{\nu-1}@{z}\diff{z} = z^{\nu}\modStruveL{\nu}@{z}} | int((z)^(nu)* StruveL(nu - 1, z), z)= (z)^(nu)* StruveL(nu, z) |
Integrate[(z)^(\[Nu])* StruveL[\[Nu]- 1, z], z]= (z)^(\[Nu])* StruveL[\[Nu], z] |
Failure | Successful | Skip | - |
| 11.7.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int z^{-\nu}\modStruveL{\nu+1}@{z}\diff{z} = z^{-\nu}\modStruveL{\nu}@{z}-\frac{2^{-\nu}z}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}} | int((z)^(- nu)* StruveL(nu + 1, z), z)= (z)^(- nu)* StruveL(nu, z)-((2)^(- nu)* z)/(sqrt(Pi)*GAMMA(nu +(3)/(2))) |
Integrate[(z)^(- \[Nu])* StruveL[\[Nu]+ 1, z], z]= (z)^(- \[Nu])* StruveL[\[Nu], z]-Divide[(2)^(- \[Nu])* z,Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]] |
Successful | Successful | - | - |
| 11.7.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{\nu}(z) = \int_{0}^{z}t^{\nu}\StruveH{\nu}@{t}\diff{t}} | f[nu]*(z)= int((t)^(nu)* StruveH(nu, t), t = 0..z) |
Subscript[f, \[Nu]]*(z)= Integrate[(t)^(\[Nu])* StruveH[\[Nu], t], {t, 0, z}] |
Failure | Failure | Skip | Error |
| 11.7.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{\nu+1}(z) = (2\nu+1)f_{\nu}(z)-z^{\nu+1}\StruveH{\nu}@{z}+\frac{(\tfrac{1}{2}z^{2})^{\nu+1}}{(\nu+1)\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}} | f[nu + 1]*(z)=(2*nu + 1)* f[nu]*(z)- (z)^(nu + 1)* StruveH(nu, z)+(((1)/(2)*(z)^(2))^(nu + 1))/((nu + 1)*sqrt(Pi)*GAMMA(nu +(3)/(2))) |
Subscript[f, \[Nu]+ 1]*(z)=(2*\[Nu]+ 1)* Subscript[f, \[Nu]]*(z)- (z)^(\[Nu]+ 1)* StruveH[\[Nu], z]+Divide[(Divide[1,2]*(z)^(2))^(\[Nu]+ 1),(\[Nu]+ 1)*Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]] |
Failure | Failure | Fail .588297823+3.112391650*I <- {z = 2^(1/2)+I*2^(1/2), f[nu] = 2^(1/2)+I*2^(1/2), f[nu+1] = 2^(1/2)+I*2^(1/2), nu = -1/2}4.588297821-.8876083477*I <- {z = 2^(1/2)+I*2^(1/2), f[nu] = 2^(1/2)+I*2^(1/2), f[nu+1] = 2^(1/2)-I*2^(1/2), nu = -1/2}.588297823-4.887608346*I <- {z = 2^(1/2)+I*2^(1/2), f[nu] = 2^(1/2)+I*2^(1/2), f[nu+1] = -2^(1/2)-I*2^(1/2), nu = -1/2}-3.411702175-.8876083477*I <- {z = 2^(1/2)+I*2^(1/2), f[nu] = 2^(1/2)+I*2^(1/2), f[nu+1] = -2^(1/2)+I*2^(1/2), nu = -1/2}... skip entries to safe data |
Error |
| 11.7.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi/2}\StruveH{\nu}@{z\sin@@{\theta}}\frac{(\sin@@{\theta})^{\nu+1}}{(\cos@@{\theta})^{2\nu}}\diff{\theta} = \frac{2^{-\nu}}{\sqrt{\pi}}\EulerGamma@{\tfrac{1}{2}-\nu}z^{\nu-1}(1-\cos@@{z})} | int(StruveH(nu, z*sin(theta))*((sin(theta))^(nu + 1))/((cos(theta))^(2*nu)), theta = 0..Pi/ 2)=((2)^(- nu))/(sqrt(Pi))*GAMMA((1)/(2)- nu)*(z)^(nu - 1)*(1 - cos(z)) |
Integrate[StruveH[\[Nu], z*Sin[\[Theta]]]*Divide[(Sin[\[Theta]])^(\[Nu]+ 1),(Cos[\[Theta]])^(2*\[Nu])], {\[Theta], 0, Pi/ 2}]=Divide[(2)^(- \[Nu]),Sqrt[Pi]]*Gamma[Divide[1,2]- \[Nu]]*(z)^(\[Nu]- 1)*(1 - Cos[z]) |
Successful | Failure | - | Error |
| 11.7#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\StruveH{0}@{t}\,\frac{\diff{t}}{t} = \tfrac{1}{2}\pi} | int(StruveH(0, t)*(1)/(t), t = 0..infinity)=(1)/(2)*Pi |
Integrate[StruveH[0, t]*Divide[1,t], {t, 0, Infinity}]=Divide[1,2]*Pi |
Successful | Successful | - | - |
| 11.7#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\StruveH{1}@{t}\,\frac{\diff{t}}{t^{2}} = \tfrac{1}{4}\pi} | int(StruveH(1, t)*(1)/((t)^(2)), t = 0..infinity)=(1)/(4)*Pi |
Integrate[StruveH[1, t]*Divide[1,(t)^(2)], {t, 0, Infinity}]=Divide[1,4]*Pi |
Successful | Successful | - | - |
| 11.7.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\StruveH{\nu}@{t}\diff{t} = -\cot@{\tfrac{1}{2}\pi\nu}} | int(StruveH(nu, t), t = 0..infinity)= - cot((1)/(2)*Pi*nu) |
Integrate[StruveH[\[Nu], t], {t, 0, Infinity}]= - Cot[Divide[1,2]*Pi*\[Nu]] |
Successful | Failure | - | Error |
| 11.7.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{-\nu-1}\StruveH{\nu}@{t}\diff{t} = \frac{\pi}{2^{\nu+1}\EulerGamma@{\nu+1}}} | int((t)^(- nu - 1)* StruveH(nu, t), t = 0..infinity)=(Pi)/((2)^(nu + 1)* GAMMA(nu + 1)) |
Integrate[(t)^(- \[Nu]- 1)* StruveH[\[Nu], t], {t, 0, Infinity}]=Divide[Pi,(2)^(\[Nu]+ 1)* Gamma[\[Nu]+ 1]] |
Successful | Failure | - | Error |
| 11.7.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu-\nu-1}\StruveH{\nu}@{t}\diff{t} = \frac{\EulerGamma@{\tfrac{1}{2}\mu}2^{\mu-\nu-1}\tan@{\tfrac{1}{2}\pi\mu}}{\EulerGamma@{\nu-\tfrac{1}{2}\mu+1}}} | int((t)^(mu - nu - 1)* StruveH(nu, t), t = 0..infinity)=(GAMMA((1)/(2)*mu)*(2)^(mu - nu - 1)* tan((1)/(2)*Pi*mu))/(GAMMA(nu -(1)/(2)*mu + 1)) |
Integrate[(t)^(\[Mu]- \[Nu]- 1)* StruveH[\[Nu], t], {t, 0, Infinity}]=Divide[Gamma[Divide[1,2]*\[Mu]]*(2)^(\[Mu]- \[Nu]- 1)* Tan[Divide[1,2]*Pi*\[Mu]],Gamma[\[Nu]-Divide[1,2]*\[Mu]+ 1]] |
Successful | Failure | - | Error |
| 11.7.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{-\mu-\nu}\StruveH{\mu}@{t}\StruveH{\nu}@{t}\diff{t} = \frac{\sqrt{\pi}\EulerGamma@{\mu+\nu}}{2^{\mu+\nu}\EulerGamma@{\mu+\nu+\tfrac{1}{2}}\EulerGamma@{\mu+\tfrac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}} | int((t)^(- mu - nu)* StruveH(mu, t)*StruveH(nu, t), t = 0..infinity)=(sqrt(Pi)*GAMMA(mu + nu))/((2)^(mu + nu)* GAMMA(mu + nu +(1)/(2))*GAMMA(mu +(1)/(2))*GAMMA(nu +(1)/(2))) |
Integrate[(t)^(- \[Mu]- \[Nu])* StruveH[\[Mu], t]*StruveH[\[Nu], t], {t, 0, Infinity}]=Divide[Sqrt[Pi]*Gamma[\[Mu]+ \[Nu]],(2)^(\[Mu]+ \[Nu])* Gamma[\[Mu]+ \[Nu]+Divide[1,2]]*Gamma[\[Mu]+Divide[1,2]]*Gamma[\[Nu]+Divide[1,2]]] |
Error | Failure | - | Error |
| 11.7.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\StruveH{0}@{t}\diff{t} = \frac{2}{\pi\sqrt{1+a^{2}}}\ln@{\frac{1+\sqrt{1+a^{2}}}{a}}} | int(exp(- a*t)*StruveH(0, t), t = 0..infinity)=(2)/(Pi*sqrt(1 + (a)^(2)))*ln((1 +sqrt(1 + (a)^(2)))/(a)) |
Integrate[Exp[- a*t]*StruveH[0, t], {t, 0, Infinity}]=Divide[2,Pi*Sqrt[1 + (a)^(2)]]*Log[Divide[1 +Sqrt[1 + (a)^(2)],a]] |
Failure | Failure | Skip | Error |
| 11.7.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\StruveH{1}@{t}\diff{t} = \frac{2}{\pi a}-\frac{2a}{\pi\sqrt{1+a^{2}}}\ln@{\frac{1+\sqrt{1+a^{2}}}{a}}} | int(exp(- a*t)*StruveH(1, t), t = 0..infinity)=(2)/(Pi*a)-(2*a)/(Pi*sqrt(1 + (a)^(2)))*ln((1 +sqrt(1 + (a)^(2)))/(a)) |
Integrate[Exp[- a*t]*StruveH[1, t], {t, 0, Infinity}]=Divide[2,Pi*a]-Divide[2*a,Pi*Sqrt[1 + (a)^(2)]]*Log[Divide[1 +Sqrt[1 + (a)^(2)],a]] |
Failure | Failure | Skip | Error |
| 11.7.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\modStruveL{0}@{t}\diff{t} = \frac{2}{\pi\sqrt{a^{2}\!-\!1}}\asin@{\frac{1}{a}}} | int(exp(- a*t)*StruveL(0, t), t = 0..infinity)=(2)/(Pi*sqrt((a)^(2)- 1))*arcsin((1)/(a)) |
Integrate[Exp[- a*t]*StruveL[0, t], {t, 0, Infinity}]=Divide[2,Pi*Sqrt[(a)^(2)- 1]]*ArcSin[Divide[1,a]] |
Failure | Failure | Skip | Error |
| 11.7#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle = \frac{2a}{\pi\sqrt{a^{2}\!-\!1}}\atan@{\frac{1}{\sqrt{a^{2}\!-\!1}}}-\frac{2}{\pi a}} | =(2*a)/(Pi*sqrt((a)^(2)- 1))*arctan((1)/(sqrt((a)^(2)- 1)))-(2)/(Pi*a) |
=Divide[2*a,Pi*Sqrt[(a)^(2)- 1]]*ArcTan[Divide[1,Sqrt[(a)^(2)- 1]]]-Divide[2,Pi*a] |
Error | Failure | - | Error |
| 11.9.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}+\left(1-\frac{\nu^{2}}{z^{2}}\right)w = z^{\mu-1}} | diff(w, [z$(2)])+(1)/(z)*diff(w, z)+(1 -((nu)^(2))/((z)^(2)))* w = (z)^(mu - 1) |
D[w, {z, 2}]+Divide[1,z]*D[w, z]+(1 -Divide[(\[Nu])^(2),(z)^(2)])* w = (z)^(\[Mu]- 1) |
Failure | Failure | Fail -.1150287995-.4235009013*I <- {mu = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-.380733971+.363721811*I <- {mu = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-37.31009604-.1600773484*I <- {mu = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}2.846320383+2.784324879*I <- {mu = 2^(1/2)+I*2^(1/2), 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 |
Error |
| 11.9.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \Lommels{\mu}{\nu}@{z}+A\BesselJ{\nu}@{z}+B\BesselY{\nu}@{z}} | w = LommelS1(mu, nu, z)+ A*BesselJ(nu, z)+ B*BesselY(nu, z) |
Error |
Failure | Error | Skip | - |
| 11.9.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Lommels{\mu}{\nu}@{z} = z^{\mu+1}\sum_{k=0}^{\infty}(-1)^{k}\frac{z^{2k}}{a_{k+1}(\mu,\nu)}} | LommelS1(mu, nu, z)= (z)^(mu + 1)* sum((- 1)^(k)*((z)^(2*k))/(a[k + 1]*(mu , nu)), k = 0..infinity) |
Error |
Failure | Error | Skip | - |
| 11.9.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LommelS{\mu}{\nu}@{z} = \Lommels{\mu}{\nu}@{z}+2^{\mu-1}\EulerGamma@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}}\EulerGamma@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2}}\*\left(\sin@{\tfrac{1}{2}(\mu-\nu)\pi}\,\BesselJ{\nu}@{z}-\cos@{\tfrac{1}{2}(\mu-\nu)\pi}\,\BesselY{\nu}@{z}\right)} | LommelS2(mu, nu, z)= LommelS1(mu, nu, z)+ (2)^(mu - 1)* GAMMA((1)/(2)*mu +(1)/(2)*nu +(1)/(2))*GAMMA((1)/(2)*mu -(1)/(2)*nu +(1)/(2))*(sin((1)/(2)*(mu - nu)* Pi)*BesselJ(nu, z)- cos((1)/(2)*(mu - nu)* Pi)*BesselY(nu, z)) |
Error |
Successful | Error | - | - |
| 11.9#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Lommels{\mu}{-\nu}@{z} = \Lommels{\mu}{\nu}@{z}} | LommelS1(mu, - nu, z)= LommelS1(mu, nu, z) |
Error |
Successful | Error | - | - |
| 11.9#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LommelS{\mu}{-\nu}@{z} = \LommelS{\mu}{\nu}@{z}} | LommelS2(mu, - nu, z)= LommelS2(mu, nu, z) |
Error |
Successful | Error | - | - |
| 11.9.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Lommels{\mu}{\nu}@{z} = 2^{\mu+1}\sum_{k=0}^{\infty}\*\frac{(2k+\mu+1)\EulerGamma@{k+\mu+1}}{k!(2k+\mu-\nu+1)(2k+\mu+\nu+1)}\BesselJ{2k+\mu+1}@{z}} | LommelS1(mu, nu, z)= (2)^(mu + 1)* sum(*((2*k + mu + 1)* GAMMA(k + mu + 1))/(factorial(k)*(2*k + mu - nu + 1)*(2*k + mu + nu + 1))*BesselJ(2*k + mu + 1, z), k = 0..infinity) |
Error |
Error | Error | - | - |
| 11.9.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Lommels{\mu}{\nu}@{z} = 2^{(\mu+\nu-1)/2}\EulerGamma@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}}z^{(\mu+1-\nu)/2}\*\sum_{k=0}^{\infty}\frac{(\tfrac{1}{2}z)^{k}}{k!(2k+\mu-\nu+1)}\BesselJ{k+\frac{1}{2}(\mu+\nu+1)}@{z}} | LommelS1(mu, nu, z)= (2)^((mu + nu - 1)/ 2)* GAMMA((1)/(2)*mu +(1)/(2)*nu +(1)/(2))*(z)^((mu + 1 - nu)/ 2)* sum((((1)/(2)*z)^(k))/(factorial(k)*(2*k + mu - nu + 1))*BesselJ(k +(1)/(2)*(mu + nu + 1), z), k = 0..infinity) |
Error |
Failure | Error | Skip | - |
| 11.10.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AngerJ{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{\nu\theta-z\sin@@{\theta}}\diff{\theta}} | AngerJ(nu, z)=(1)/(Pi)*int(cos(nu*theta - z*sin(theta)), theta = 0..Pi) |
AngerJ[\[Nu], z]=Divide[1,Pi]*Integrate[Cos[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, Pi}] |
Failure | Failure | Skip | Error |
| 11.10.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\sin@{\nu\theta-z\sin@@{\theta}}\diff{\theta}} | WeberE(nu, z)=(1)/(Pi)*int(sin(nu*theta - z*sin(theta)), theta = 0..Pi) |
WeberE[\[Nu], z]=Divide[1,Pi]*Integrate[Sin[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, Pi}] |
Failure | Failure | Skip | Error |
| 11.10.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\pi}\int_{0}^{2\pi}\cos@{\nu\theta-z\sin@@{\theta}}\diff{\theta} = (1+\cos@{2\pi\nu})\,\AngerJ{\nu}@{z}+\sin@{2\pi\nu}\WeberE{\nu}@{z}} | (1)/(Pi)*int(cos(nu*theta - z*sin(theta)), theta = 0..2*Pi)=(1 + cos(2*Pi*nu))* AngerJ(nu, z)+ sin(2*Pi*nu)*WeberE(nu, z) |
Divide[1,Pi]*Integrate[Cos[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, 2*Pi}]=(1 + Cos[2*Pi*\[Nu]])* AngerJ[\[Nu], z]+ Sin[2*Pi*\[Nu]]*WeberE[\[Nu], z] |
Failure | Failure | Skip | Error |
| 11.10.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AngerJ{\nu}@{z} = \cos@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)+\sin@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)} | AngerJ(nu, z)= cos((1)/(2)*Pi*nu)*S[1]*(nu , z)+ sin((1)/(2)*Pi*nu)*S[2]*(nu , z) |
AngerJ[\[Nu], z]= Cos[Divide[1,2]*Pi*\[Nu]]*Subscript[S, 1]*(\[Nu], z)+ Sin[Divide[1,2]*Pi*\[Nu]]*Subscript[S, 2]*(\[Nu], z) |
Failure | Failure | Error | Error |
| 11.10.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{\nu}@{z} = \sin@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)-\cos@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)} | WeberE(nu, z)= sin((1)/(2)*Pi*nu)*S[1]*(nu , z)- cos((1)/(2)*Pi*nu)*S[2]*(nu , z) |
WeberE[\[Nu], z]= Sin[Divide[1,2]*Pi*\[Nu]]*Subscript[S, 1]*(\[Nu], z)- Cos[Divide[1,2]*Pi*\[Nu]]*Subscript[S, 2]*(\[Nu], z) |
Failure | Failure | Error | Error |
| 11.10.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{1}(\nu,z) = \sum_{k=0}^{\infty}\frac{(-1)^{k}(\tfrac{1}{2}z)^{2k}}{\EulerGamma@{k\!+\!\tfrac{1}{2}\nu+1}\EulerGamma@{k\!-\!\tfrac{1}{2}\nu\!+\!1}}} | S[1]*(nu , z)= sum(((- 1)^(k)*((1)/(2)*z)^(2*k))/(GAMMA(k +(1)/(2)*nu + 1)*GAMMA(k -(1)/(2)*nu + 1)), k = 0..infinity) |
Subscript[S, 1]*(\[Nu], z)= Sum[Divide[(- 1)^(k)*(Divide[1,2]*z)^(2*k),Gamma[k +Divide[1,2]*\[Nu]+ 1]*Gamma[k -Divide[1,2]*\[Nu]+ 1]], {k, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 11.10.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{2}(\nu,z) = \sum_{k=0}^{\infty}\frac{(-1)^{k}(\tfrac{1}{2}z)^{2k+1}}{\EulerGamma@{k\!+\!\tfrac{1}{2}\nu\!+\!\tfrac{3}{2}}\EulerGamma@{k\!-\!\tfrac{1}{2}\nu\!+\!\tfrac{3}{2}}}} | S[2]*(nu , z)= sum(((- 1)^(k)*((1)/(2)*z)^(2*k + 1))/(GAMMA(k +(1)/(2)*nu +(3)/(2))*GAMMA(k -(1)/(2)*nu +(3)/(2))), k = 0..infinity) |
Subscript[S, 2]*(\[Nu], z)= Sum[Divide[(- 1)^(k)*(Divide[1,2]*z)^(2*k + 1),Gamma[k +Divide[1,2]*\[Nu]+Divide[3,2]]*Gamma[k -Divide[1,2]*\[Nu]+Divide[3,2]]], {k, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 11.10#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AngerJ{\nu}@{-z} = \AngerJ{-\nu}@{z}} | AngerJ(nu, - z)= AngerJ(- nu, z) |
AngerJ[\[Nu], - z]= AngerJ[- \[Nu], z] |
Successful | Successful | - | - |
| 11.10#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{\nu}@{-z} = -\WeberE{-\nu}@{z}} | WeberE(nu, - z)= - WeberE(- nu, z) |
WeberE[\[Nu], - z]= - WeberE[- \[Nu], z] |
Successful | Successful | - | - |
| 11.10.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{\pi\nu}\,\AngerJ{\nu}@{z} = \cos@{\pi\nu}\,\WeberE{\nu}@{z}-\WeberE{-\nu}@{z}} | sin(Pi*nu)*AngerJ(nu, z)= cos(Pi*nu)*WeberE(nu, z)- WeberE(- nu, z) |
Sin[Pi*\[Nu]]*AngerJ[\[Nu], z]= Cos[Pi*\[Nu]]*WeberE[\[Nu], z]- WeberE[- \[Nu], z] |
Successful | Failure | - | Error |
| 11.10.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{\pi\nu}\,\WeberE{\nu}@{z} = \AngerJ{-\nu}@{z}-\cos@{\pi\nu}\,\AngerJ{\nu}@{z}} | sin(Pi*nu)*WeberE(nu, z)= AngerJ(- nu, z)- cos(Pi*nu)*AngerJ(nu, z) |
Sin[Pi*\[Nu]]*WeberE[\[Nu], z]= AngerJ[- \[Nu], z]- Cos[Pi*\[Nu]]*AngerJ[\[Nu], z] |
Successful | Failure | - | Error |
| 11.10.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AngerJ{\nu}@{z} = \frac{\sin@{\pi\nu}}{\pi}(\Lommels{0}{\nu}@{z}-\nu\Lommels{-1}{\nu}@{z})} | AngerJ(nu, z)=(sin(Pi*nu))/(Pi)*(LommelS1(0, nu, z)- nu*LommelS1(- 1, nu, z)) |
Error |
Successful | Error | - | - |
| 11.10.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{\nu}@{z} = -\frac{1}{\pi}(1+\cos@{\pi\nu})\Lommels{0}{\nu}@{z}\\ -\frac{\nu}{\pi}(1-\cos@{\pi\nu})\Lommels{-1}{\nu}@{z}} | WeberE(nu, z)= -(1)/(Pi)*(1 + cos(Pi*nu))* LommelS1(0, nu, z)-(nu)/(Pi)*(1 - cos(Pi*nu))* LommelS1(- 1, nu, z) |
Error |
Successful | Error | - | - |
| 11.10.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\cos@@{z}-A_{-}(\chi)\sin@@{z})} | WeberE((1)/(2), z)=((1)/(2)*Pi*z)^(-(1)/(2))*(A[+]*(chi)*cos(z)- A[-]*(chi)*sin(z)) |
WeberE[Divide[1,2], z]=(Divide[1,2]*Pi*z)^(-Divide[1,2])*(Subscript[A, +]*(\[Chi])*Cos[z]- Subscript[A, -]*(\[Chi])*Sin[z]) |
Error | Error | - | - |
| 11.10.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\WeberE{-\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\sin@@{z}+A_{-}(\chi)\cos@@{z})} | - WeberE(-(1)/(2), z)=((1)/(2)*Pi*z)^(-(1)/(2))*(A[+]*(chi)*sin(z)+ A[-]*(chi)*cos(z)) |
- WeberE[-Divide[1,2], z]=(Divide[1,2]*Pi*z)^(-Divide[1,2])*(Subscript[A, +]*(\[Chi])*Sin[z]+ Subscript[A, -]*(\[Chi])*Cos[z]) |
Error | Error | - | - |
| 11.10#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{+}(\chi) = \Fresnelcosint@{\chi}+\Fresnelsinint@{\chi}} | A[+]*(chi)= FresnelC(chi)+ FresnelS(chi) |
Subscript[A, +]*(\[Chi])= FresnelC[\[Chi]]+ FresnelS[\[Chi]] |
Error | Failure | - | Error |
| 11.10#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-}(\chi) = \Fresnelcosint@{\chi}-\Fresnelsinint@{\chi}} | A[-]*(chi)= FresnelC(chi)- FresnelS(chi) |
Subscript[A, -]*(\[Chi])= FresnelC[\[Chi]]- FresnelS[\[Chi]] |
Error | Failure | - | Error |
| 11.10.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{n}@{z} = -\StruveH{n}@{z}+\frac{1}{\pi}\sum_{k=0}^{m_{1}}\frac{\EulerGamma@{k+\tfrac{1}{2}}}{\EulerGamma@{n\!+\!\tfrac{1}{2}\!-\!k}}(\tfrac{1}{2}z)^{n-2k-1}} | WeberE(n, z)= - StruveH(n, z)+(1)/(Pi)*sum((GAMMA(k +(1)/(2)))/(GAMMA(n +(1)/(2)- k))*((1)/(2)*z)^(n - 2*k - 1), k = 0..m[1]) |
WeberE[n, z]= - StruveH[n, z]+Divide[1,Pi]*Sum[Divide[Gamma[k +Divide[1,2]],Gamma[n +Divide[1,2]- k]]*(Divide[1,2]*z)^(n - 2*k - 1), {k, 0, Subscript[m, 1]}] |
Failure | Failure | Skip | Error |
| 11.10.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{-n}@{z} = -\StruveH{-n}@{z}+\frac{(-1)^{n+1}}{\pi}\sum_{k=0}^{m_{2}}\frac{\EulerGamma@{n\!-\!k\!-\!\tfrac{1}{2}}}{\EulerGamma@{k+\tfrac{3}{2}}}(\tfrac{1}{2}z)^{-n+2k+1}} | WeberE(- n, z)= - StruveH(- n, z)+((- 1)^(n + 1))/(Pi)*sum((GAMMA(n - k -(1)/(2)))/(GAMMA(k +(3)/(2)))*((1)/(2)*z)^(- n + 2*k + 1), k = 0..m[2]) |
WeberE[- n, z]= - StruveH[- n, z]+Divide[(- 1)^(n + 1),Pi]*Sum[Divide[Gamma[n - k -Divide[1,2]],Gamma[k +Divide[3,2]]]*(Divide[1,2]*z)^(- n + 2*k + 1), {k, 0, Subscript[m, 2]}] |
Failure | Failure | Skip | Error |
| 11.10#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m_{1} = \floor{\tfrac{1}{2}n-\tfrac{1}{2}}} | m[1]= floor((1)/(2)*n -(1)/(2)) |
Subscript[m, 1]= Floor[Divide[1,2]*n -Divide[1,2]] |
Failure | Failure | Fail 1.414213562+1.414213562*I <- {m[1] = 2^(1/2)+I*2^(1/2), n = 1}1.414213562+1.414213562*I <- {m[1] = 2^(1/2)+I*2^(1/2), n = 2}.414213562+1.414213562*I <- {m[1] = 2^(1/2)+I*2^(1/2), n = 3}1.414213562-1.414213562*I <- {m[1] = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Error |
| 11.10#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m_{2} = \ceiling{\tfrac{1}{2}n-\tfrac{3}{2}}} | m[2]= ceil((1)/(2)*n -(3)/(2)) |
Subscript[m, 2]= Ceiling[Divide[1,2]*n -Divide[3,2]] |
Failure | Failure | Fail 2.414213562+1.414213562*I <- {m[2] = 2^(1/2)+I*2^(1/2), n = 1}1.414213562+1.414213562*I <- {m[2] = 2^(1/2)+I*2^(1/2), n = 2}1.414213562+1.414213562*I <- {m[2] = 2^(1/2)+I*2^(1/2), n = 3}2.414213562-1.414213562*I <- {m[2] = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Error |
| 11.10.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AngerJ{n}@{z} = \BesselJ{n}@{z}} | AngerJ(n, z)= BesselJ(n, z) |
AngerJ[n, z]= BesselJ[n, z] |
Failure | Failure | Successful | Error |
| 11.10.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AngerJ{\nu-1}@{z}+\AngerJ{\nu+1}@{z} = \frac{2\nu}{z}\AngerJ{\nu}@{z}-\frac{2}{\pi z}\sin@{\pi\nu}} | AngerJ(nu - 1, z)+ AngerJ(nu + 1, z)=(2*nu)/(z)*AngerJ(nu, z)-(2)/(Pi*z)*sin(Pi*nu) |
AngerJ[\[Nu]- 1, z]+ AngerJ[\[Nu]+ 1, z]=Divide[2*\[Nu],z]*AngerJ[\[Nu], z]-Divide[2,Pi*z]*Sin[Pi*\[Nu]] |
Failure | Failure | Successful | Error |
| 11.10.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{\nu-1}@{z}+\WeberE{\nu+1}@{z} = \frac{2\nu}{z}\WeberE{\nu}@{z}-\frac{2}{\pi z}(1-\cos@{\pi\nu})} | WeberE(nu - 1, z)+ WeberE(nu + 1, z)=(2*nu)/(z)*WeberE(nu, z)-(2)/(Pi*z)*(1 - cos(Pi*nu)) |
WeberE[\[Nu]- 1, z]+ WeberE[\[Nu]+ 1, z]=Divide[2*\[Nu],z]*WeberE[\[Nu], z]-Divide[2,Pi*z]*(1 - Cos[Pi*\[Nu]]) |
Failure | Failure | Successful | Error |
| 11.10.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\AngerJ{\nu}'@{z} = \AngerJ{\nu-1}@{z}-\AngerJ{\nu+1}@{z}} | 2*subs( temp=z, diff( AngerJ(nu, temp), temp$(1) ) )= AngerJ(nu - 1, z)- AngerJ(nu + 1, z) |
2*(D[AngerJ[\[Nu], temp], {temp, 1}]/.temp-> z)= AngerJ[\[Nu]- 1, z]- AngerJ[\[Nu]+ 1, z] |
Failure | Successful | Successful | - |
| 11.10.E35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\WeberE{\nu}'@{z} = \WeberE{\nu-1}@{z}-\WeberE{\nu+1}@{z}} | 2*subs( temp=z, diff( WeberE(nu, temp), temp$(1) ) )= WeberE(nu - 1, z)- WeberE(nu + 1, z) |
2*(D[WeberE[\[Nu], temp], {temp, 1}]/.temp-> z)= WeberE[\[Nu]- 1, z]- WeberE[\[Nu]+ 1, z] |
Failure | Successful | Successful | - |
| 11.10.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\AngerJ{\nu}'@{z}+\nu\AngerJ{\nu}@{z} = + z\AngerJ{\nu- 1}@{z}+\frac{\sin@{\pi\nu}}{\pi}} | z*subs( temp=z, diff( AngerJ(nu, temp), temp$(1) ) )+ nu*AngerJ(nu, z)= + z*AngerJ(nu - 1, z)+(sin(Pi*nu))/(Pi) |
z*(D[AngerJ[\[Nu], temp], {temp, 1}]/.temp-> z)+ \[Nu]*AngerJ[\[Nu], z]= + z*AngerJ[\[Nu]- 1, z]+Divide[Sin[Pi*\[Nu]],Pi] |
Failure | Failure | Successful | Error |
| 11.10.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\AngerJ{\nu}'@{z}-\nu\AngerJ{\nu}@{z} = - z\AngerJ{\nu+ 1}@{z}-\frac{\sin@{\pi\nu}}{\pi}} | z*subs( temp=z, diff( AngerJ(nu, temp), temp$(1) ) )- nu*AngerJ(nu, z)= - z*AngerJ(nu + 1, z)-(sin(Pi*nu))/(Pi) |
z*(D[AngerJ[\[Nu], temp], {temp, 1}]/.temp-> z)- \[Nu]*AngerJ[\[Nu], z]= - z*AngerJ[\[Nu]+ 1, z]-Divide[Sin[Pi*\[Nu]],Pi] |
Successful | Failure | - | Error |
| 11.10.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\WeberE{\nu}'@{z}+\nu\WeberE{\nu}@{z} = + z\WeberE{\nu- 1}@{z}+\frac{(1-\cos@{\pi\nu})}{\pi}} | z*subs( temp=z, diff( WeberE(nu, temp), temp$(1) ) )+ nu*WeberE(nu, z)= + z*WeberE(nu - 1, z)+(1 - cos(Pi*nu))/(Pi) |
z*(D[WeberE[\[Nu], temp], {temp, 1}]/.temp-> z)+ \[Nu]*WeberE[\[Nu], z]= + z*WeberE[\[Nu]- 1, z]+Divide[1 - Cos[Pi*\[Nu]],Pi] |
Failure | Failure | Successful | Error |
| 11.10.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\WeberE{\nu}'@{z}-\nu\WeberE{\nu}@{z} = - z\WeberE{\nu+ 1}@{z}-\frac{(1-\cos@{\pi\nu})}{\pi}} | z*subs( temp=z, diff( WeberE(nu, temp), temp$(1) ) )- nu*WeberE(nu, z)= - z*WeberE(nu + 1, z)-(1 - cos(Pi*nu))/(Pi) |
z*(D[WeberE[\[Nu], temp], {temp, 1}]/.temp-> z)- \[Nu]*WeberE[\[Nu], z]= - z*WeberE[\[Nu]+ 1, z]-Divide[1 - Cos[Pi*\[Nu]],Pi] |
Successful | Failure | - | Error |
| 11.11.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu = \sqrt{1-\lambda^{2}}-\ln@{\frac{1+\sqrt{1-\lambda^{2}}}{\lambda}}} | mu =sqrt(1 - (lambda)^(2))- ln((1 +sqrt(1 - (lambda)^(2)))/(lambda)) |
\[Mu]=Sqrt[1 - (\[Lambda])^(2)]- Log[Divide[1 +Sqrt[1 - (\[Lambda])^(2)],\[Lambda]]] |
Failure | Failure | Fail .1801572199+1.430482725*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2)}.1801572199-1.397944399*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2)}-2.648269904-1.397944399*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = -2^(1/2)-I*2^(1/2)}-2.648269904+1.430482725*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Error |