Results of Airy and Related Functions
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| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 9.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \AiryAi@{z},\;\AiryBi@{z},\;\AiryAi@{ze^{- 2\pi\iunit/3}}} | w = AiryAi(z), AiryBi(z), AiryAi(z*exp(- 2*Pi*I/ 3)) |
w = AiryAi[z], AiryBi[z], AiryAi[z*Exp[- 2*Pi*I/ 3]] |
Failure | Failure | Error | Error |
| 9.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \AiryAi@{z},\;\AiryBi@{z},\;\AiryAi@{ze^{+ 2\pi\iunit/3}}} | w = AiryAi(z), AiryBi(z), AiryAi(z*exp(+ 2*Pi*I/ 3)) |
w = AiryAi[z], AiryBi[z], AiryAi[z*Exp[+ 2*Pi*I/ 3]] |
Failure | Failure | Error | Error |
| 9.2.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{0} = \frac{1}{3^{2/3}\EulerGamma@{\tfrac{2}{3}}}} | AiryAi(0)=(1)/((3)^(2/ 3)* GAMMA((2)/(3))) |
AiryAi[0]=Divide[1,(3)^(2/ 3)* Gamma[Divide[2,3]]] |
Successful | Successful | - | - |
| 9.2.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi'@{0} = -\frac{1}{3^{1/3}\EulerGamma@{\tfrac{1}{3}}}} | subs( temp=0, diff( AiryAi(temp), temp$(1) ) )= -(1)/((3)^(1/ 3)* GAMMA((1)/(3))) |
(D[AiryAi[temp], {temp, 1}]/.temp-> 0)= -Divide[1,(3)^(1/ 3)* Gamma[Divide[1,3]]] |
Successful | Successful | - | - |
| 9.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi@{0} = \frac{1}{3^{1/6}\EulerGamma@{\tfrac{2}{3}}}} | AiryBi(0)=(1)/((3)^(1/ 6)* GAMMA((2)/(3))) |
AiryBi[0]=Divide[1,(3)^(1/ 6)* Gamma[Divide[2,3]]] |
Successful | Successful | - | - |
| 9.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi'@{0} = \frac{3^{1/6}}{\EulerGamma@{\tfrac{1}{3}}}} | subs( temp=0, diff( AiryBi(temp), temp$(1) ) )=((3)^(1/ 6))/(GAMMA((1)/(3))) |
(D[AiryBi[temp], {temp, 1}]/.temp-> 0)=Divide[(3)^(1/ 6),Gamma[Divide[1,3]]] |
Successful | Successful | - | - |
| 9.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\AiryAi@{z},\AiryBi@{z}} = \frac{1}{\pi}} | (AiryAi(z))*diff(AiryBi(z), z)-diff(AiryAi(z), z)*(AiryBi(z))=(1)/(Pi) |
Wronskian[{AiryAi[z], AiryBi[z]}, z]=Divide[1,Pi] |
Failure | Successful | Successful | - |
| 9.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\AiryAi@{z},\AiryAi@{ze^{- 2\pi i/3}}} = \frac{e^{+\pi i/6}}{2\pi}} | (AiryAi(z))*diff(AiryAi(z*exp(- 2*Pi*I/ 3)), z)-diff(AiryAi(z), z)*(AiryAi(z*exp(- 2*Pi*I/ 3)))=(exp(+ Pi*I/ 6))/(2*Pi) |
Wronskian[{AiryAi[z], AiryAi[z*Exp[- 2*Pi*I/ 3]]}, z]=Divide[Exp[+ Pi*I/ 6],2*Pi] |
Failure | Successful | Successful | - |
| 9.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\AiryAi@{z},\AiryAi@{ze^{+ 2\pi i/3}}} = \frac{e^{-\pi i/6}}{2\pi}} | (AiryAi(z))*diff(AiryAi(z*exp(+ 2*Pi*I/ 3)), z)-diff(AiryAi(z), z)*(AiryAi(z*exp(+ 2*Pi*I/ 3)))=(exp(- Pi*I/ 6))/(2*Pi) |
Wronskian[{AiryAi[z], AiryAi[z*Exp[+ 2*Pi*I/ 3]]}, z]=Divide[Exp[- Pi*I/ 6],2*Pi] |
Failure | Successful | Successful | - |
| 9.2.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\AiryAi@{ze^{-2\pi i/3}},\AiryAi@{ze^{2\pi i/3}}} = \frac{1}{2\pi i}} | (AiryAi(z*exp(- 2*Pi*I/ 3)))*diff(AiryAi(z*exp(2*Pi*I/ 3)), z)-diff(AiryAi(z*exp(- 2*Pi*I/ 3)), z)*(AiryAi(z*exp(2*Pi*I/ 3)))=(1)/(2*Pi*I) |
Wronskian[{AiryAi[z*Exp[- 2*Pi*I/ 3]], AiryAi[z*Exp[2*Pi*I/ 3]]}, z]=Divide[1,2*Pi*I] |
Failure | Successful | Successful | - |
| 9.2.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi@{z} = e^{-\pi i/6}\AiryAi@{ze^{-2\pi i/3}}+e^{\pi i/6}\AiryAi@{ze^{2\pi i/3}}} | AiryBi(z)= exp(- Pi*I/ 6)*AiryAi(z*exp(- 2*Pi*I/ 3))+ exp(Pi*I/ 6)*AiryAi(z*exp(2*Pi*I/ 3)) |
AiryBi[z]= Exp[- Pi*I/ 6]*AiryAi[z*Exp[- 2*Pi*I/ 3]]+ Exp[Pi*I/ 6]*AiryAi[z*Exp[2*Pi*I/ 3]] |
Failure | Successful | Successful | - |
| 9.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{ze^{- 2\pi i/3}} = \tfrac{1}{2}e^{-\pi i/3}\left(\AiryAi@{z}+ i\AiryBi@{z}\right)} | AiryAi(z*exp(- 2*Pi*I/ 3))=(1)/(2)*exp(- Pi*I/ 3)*(AiryAi(z)+ I*AiryBi(z)) |
AiryAi[z*Exp[- 2*Pi*I/ 3]]=Divide[1,2]*Exp[- Pi*I/ 3]*(AiryAi[z]+ I*AiryBi[z]) |
Failure | Successful | Successful | - |
| 9.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{ze^{+ 2\pi i/3}} = \tfrac{1}{2}e^{+\pi i/3}\left(\AiryAi@{z}- i\AiryBi@{z}\right)} | AiryAi(z*exp(+ 2*Pi*I/ 3))=(1)/(2)*exp(+ Pi*I/ 3)*(AiryAi(z)- I*AiryBi(z)) |
AiryAi[z*Exp[+ 2*Pi*I/ 3]]=Divide[1,2]*Exp[+ Pi*I/ 3]*(AiryAi[z]- I*AiryBi[z]) |
Failure | Successful | Successful | - |
| 9.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{z}+e^{-2\pi i/3}\AiryAi@{ze^{-2\pi i/3}}+e^{2\pi i/3}\AiryAi@{ze^{2\pi i/3}} = 0} | AiryAi(z)+ exp(- 2*Pi*I/ 3)*AiryAi(z*exp(- 2*Pi*I/ 3))+ exp(2*Pi*I/ 3)*AiryAi(z*exp(2*Pi*I/ 3))= 0 |
AiryAi[z]+ Exp[- 2*Pi*I/ 3]*AiryAi[z*Exp[- 2*Pi*I/ 3]]+ Exp[2*Pi*I/ 3]*AiryAi[z*Exp[2*Pi*I/ 3]]= 0 |
Failure | Successful | Successful | - |
| 9.2.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi@{z}+e^{-2\pi i/3}\AiryBi@{ze^{-2\pi i/3}}+e^{2\pi i/3}\AiryBi@{ze^{2\pi i/3}} = 0} | AiryBi(z)+ exp(- 2*Pi*I/ 3)*AiryBi(z*exp(- 2*Pi*I/ 3))+ exp(2*Pi*I/ 3)*AiryBi(z*exp(2*Pi*I/ 3))= 0 |
AiryBi[z]+ Exp[- 2*Pi*I/ 3]*AiryBi[z*Exp[- 2*Pi*I/ 3]]+ Exp[2*Pi*I/ 3]*AiryBi[z*Exp[2*Pi*I/ 3]]= 0 |
Failure | Successful | Successful | - |
| 9.2.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{-z} = e^{\pi i/3}\AiryAi@{ze^{\pi i/3}}+e^{-\pi i/3}\AiryAi@{ze^{-\pi i/3}}} | AiryAi(- z)= exp(Pi*I/ 3)*AiryAi(z*exp(Pi*I/ 3))+ exp(- Pi*I/ 3)*AiryAi(z*exp(- Pi*I/ 3)) |
AiryAi[- z]= Exp[Pi*I/ 3]*AiryAi[z*Exp[Pi*I/ 3]]+ Exp[- Pi*I/ 3]*AiryAi[z*Exp[- Pi*I/ 3]] |
Failure | Successful | Successful | - |
| 9.2.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi@{-z} = e^{-\pi i/6}\AiryAi@{ze^{\pi i/3}}+e^{\pi i/6}\AiryAi@{ze^{-\pi i/3}}} | AiryBi(- z)= exp(- Pi*I/ 6)*AiryAi(z*exp(Pi*I/ 3))+ exp(Pi*I/ 6)*AiryAi(z*exp(- Pi*I/ 3)) |
AiryBi[- z]= Exp[- Pi*I/ 6]*AiryAi[z*Exp[Pi*I/ 3]]+ Exp[Pi*I/ 6]*AiryAi[z*Exp[- Pi*I/ 3]] |
Failure | Successful | Successful | - |
| 9.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{x} = \frac{1}{\pi}\int_{0}^{\infty}\cos@{\tfrac{1}{3}t^{3}+xt}\diff{t}} | AiryAi(x)=(1)/(Pi)*int(cos((1)/(3)*(t)^(3)+ x*t), t = 0..infinity) |
AiryAi[x]=Divide[1,Pi]*Integrate[Cos[Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}] |
Successful | Failure | - | Successful |
| 9.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{-x} = \frac{x^{\ifrac{1}{2}}}{\pi}\int_{-1}^{\infty}\cos@{x^{\ifrac{3}{2}}(\tfrac{1}{3}t^{3}+t^{2}-\tfrac{2}{3})}\diff{t}} | AiryAi(- x)=((x)^((1)/(2)))/(Pi)*int(cos((x)^((3)/(2))*((1)/(3)*(t)^(3)+ (t)^(2)-(2)/(3))), t = - 1..infinity) |
AiryAi[- x]=Divide[(x)^(Divide[1,2]),Pi]*Integrate[Cos[(x)^(Divide[3,2])*(Divide[1,3]*(t)^(3)+ (t)^(2)-Divide[2,3])], {t, - 1, Infinity}] |
Failure | Failure | Skip | Error |
| 9.5.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi@{x} = \frac{1}{\pi}\int_{0}^{\infty}\exp@{-{\tfrac{1}{3}}t^{3}+xt}\diff{t}+\frac{1}{\pi}\int_{0}^{\infty}\sin@{\tfrac{1}{3}t^{3}+xt}\diff{t}} | AiryBi(x)=(1)/(Pi)*int(exp(-(1)/(3)*(t)^(3)+ x*t), t = 0..infinity)+(1)/(Pi)*int(sin((1)/(3)*(t)^(3)+ x*t), t = 0..infinity) |
AiryBi[x]=Divide[1,Pi]*Integrate[Exp[-Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}]+Divide[1,Pi]*Integrate[Sin[Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 9.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{z} = \frac{1}{2\pi i}\int_{\infty e^{-\pi i/3}}^{\infty e^{\pi i/3}}\exp@{\tfrac{1}{3}t^{3}-zt}\diff{t}} | AiryAi(z)=(1)/(2*Pi*I)*int(exp((1)/(3)*(t)^(3)- z*t), t = infinity*exp(- Pi*I/ 3)..infinity*exp(Pi*I/ 3)) |
AiryAi[z]=Divide[1,2*Pi*I]*Integrate[Exp[Divide[1,3]*(t)^(3)- z*t], {t, Infinity*Exp[- Pi*I/ 3], Infinity*Exp[Pi*I/ 3]}] |
Failure | Failure | Skip | Skip |
| 9.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi@{z} = \frac{1}{2\pi}\int_{-\infty}^{\infty e^{\pi i/3}}\exp@{\tfrac{1}{3}t^{3}-zt}\diff{t}+\dfrac{1}{2\pi}\int_{-\infty}^{\infty e^{-\pi i/3}}\exp@{\tfrac{1}{3}t^{3}-zt}\diff{t}} | AiryBi(z)=(1)/(2*Pi)*int(exp((1)/(3)*(t)^(3)- z*t), t = - infinity..infinity*exp(Pi*I/ 3))+(1)/(2*Pi)*int(exp((1)/(3)*(t)^(3)- z*t), t = - infinity..infinity*exp(- Pi*I/ 3)) |
AiryBi[z]=Divide[1,2*Pi]*Integrate[Exp[Divide[1,3]*(t)^(3)- z*t], {t, - Infinity, Infinity*Exp[Pi*I/ 3]}]+Divide[1,2*Pi]*Integrate[Exp[Divide[1,3]*(t)^(3)- z*t], {t, - Infinity, Infinity*Exp[- Pi*I/ 3]}] |
Failure | Failure | Skip | Skip |
| 9.5.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{z} = \frac{\sqrt{3}}{2\pi}\int_{0}^{\infty}\exp@{-\frac{t^{3}}{3}-\frac{z^{3}}{3t^{3}}}\diff{t}} | AiryAi(z)=(sqrt(3))/(2*Pi)*int(exp(-((t)^(3))/(3)-((z)^(3))/(3*(t)^(3))), t = 0..infinity) |
AiryAi[z]=Divide[Sqrt[3],2*Pi]*Integrate[Exp[-Divide[(t)^(3),3]-Divide[(z)^(3),3*(t)^(3)]], {t, 0, Infinity}] |
Successful | Failure | - | Successful |
| 9.5.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{z} = \frac{e^{-\zeta}}{\pi}\int_{0}^{\infty}\exp@{-z^{\ifrac{1}{2}}t^{2}}\cos@{\tfrac{1}{3}t^{3}}\diff{t}} | AiryAi(z)=(exp(-(2)/(3)*(z)^((3)/(2))))/(Pi)*int(exp(- (z)^((1)/(2))* (t)^(2))*cos((1)/(3)*(t)^(3)), t = 0..infinity) |
AiryAi[z]=Divide[Exp[-Divide[2,3]*(z)^(Divide[3,2])],Pi]*Integrate[Exp[- (z)^(Divide[1,2])* (t)^(2)]*Cos[Divide[1,3]*(t)^(3)], {t, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 9.5.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{z} = \frac{e^{-\zeta}\zeta^{\ifrac{-1}{6}}}{\sqrt{\pi}(48)^{\ifrac{1}{6}}\EulerGamma@{\frac{5}{6}}}\int_{0}^{\infty}e^{-t}t^{-\ifrac{1}{6}}\left(2+\frac{t}{\zeta}\right)^{-\ifrac{1}{6}}\diff{t}} | AiryAi(z)=(exp(-(2)/(3)*(z)^((3)/(2)))*(2)/(3)*((z)^((3)/(2)))^((- 1)/(6)))/(sqrt(Pi)*(48)^((1)/(6))* GAMMA((5)/(6)))*int(exp(- t)*(t)^(-(1)/(6))*(2 +(t)/((2)/(3)*(z)^((3)/(2))))^(-(1)/(6)), t = 0..infinity) |
AiryAi[z]=Divide[Exp[-Divide[2,3]*(z)^(Divide[3,2])]*Divide[2,3]*((z)^(Divide[3,2]))^(Divide[- 1,6]),Sqrt[Pi]*(48)^(Divide[1,6])* Gamma[Divide[5,6]]]*Integrate[Exp[- t]*(t)^(-Divide[1,6])*(2 +Divide[t,Divide[2,3]*(z)^(Divide[3,2])])^(-Divide[1,6]), {t, 0, Infinity}] |
Failure | Failure | Skip | Fail
Complex[-0.014252654553766713, -0.04024893384084034] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.014252654553766713, 0.04024893384084034] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} |
| 9.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{z} = \pi^{-1}\sqrt{z/3}\modBesselK{+ 1/3}@{\zeta}} | AiryAi(z)= (Pi)^(- 1)*sqrt(z/ 3)*BesselK(+ 1/ 3, (2)/(3)*(z)^((3)/(2))) |
AiryAi[z]= (Pi)^(- 1)*Sqrt[z/ 3]*BesselK[+ 1/ 3, Divide[2,3]*(z)^(Divide[3,2])] |
Failure | Failure | Fail 2.833765278-.3039461853*I <- {z = -2^(1/2)-I*2^(1/2)}2.833765278+.3039461853*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[2.8337652800788264, -0.3039461861802381] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.8337652800788264, 0.3039461861802381] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{z} = \pi^{-1}\sqrt{z/3}\modBesselK{- 1/3}@{\zeta}} | AiryAi(z)= (Pi)^(- 1)*sqrt(z/ 3)*BesselK(- 1/ 3, (2)/(3)*(z)^((3)/(2))) |
AiryAi[z]= (Pi)^(- 1)*Sqrt[z/ 3]*BesselK[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])] |
Failure | Failure | Fail 2.833765278-.3039461853*I <- {z = -2^(1/2)-I*2^(1/2)}2.833765278+.3039461853*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[2.8337652800788264, -0.3039461861802381] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.8337652800788264, 0.3039461861802381] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pi^{-1}\sqrt{z/3}\modBesselK{+ 1/3}@{\zeta} = \tfrac{1}{3}\sqrt{z}\left(\modBesselI{-1/3}@{\zeta}-\modBesselI{1/3}@{\zeta}\right)} | (Pi)^(- 1)*sqrt(z/ 3)*BesselK(+ 1/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(3)*sqrt(z)*(BesselI(- 1/ 3, (2)/(3)*(z)^((3)/(2)))- BesselI(1/ 3, (2)/(3)*(z)^((3)/(2)))) |
(Pi)^(- 1)*Sqrt[z/ 3]*BesselK[+ 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,3]*Sqrt[z]*(BesselI[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselI[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Successful | Successful | - | - |
| 9.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pi^{-1}\sqrt{z/3}\modBesselK{- 1/3}@{\zeta} = \tfrac{1}{3}\sqrt{z}\left(\modBesselI{-1/3}@{\zeta}-\modBesselI{1/3}@{\zeta}\right)} | (Pi)^(- 1)*sqrt(z/ 3)*BesselK(- 1/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(3)*sqrt(z)*(BesselI(- 1/ 3, (2)/(3)*(z)^((3)/(2)))- BesselI(1/ 3, (2)/(3)*(z)^((3)/(2)))) |
(Pi)^(- 1)*Sqrt[z/ 3]*BesselK[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,3]*Sqrt[z]*(BesselI[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselI[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Successful | Successful | - | - |
| 9.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{3}\sqrt{z}\left(\modBesselI{-1/3}@{\zeta}-\modBesselI{1/3}@{\zeta}\right) = \tfrac{1}{2}\sqrt{z/3}e^{2\pi i/3}\HankelH{1}{1/3}@{\zeta e^{\pi i/2}}} | (1)/(3)*sqrt(z)*(BesselI(- 1/ 3, (2)/(3)*(z)^((3)/(2)))- BesselI(1/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*sqrt(z/ 3)*exp(2*Pi*I/ 3)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2)) |
Divide[1,3]*Sqrt[z]*(BesselI[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselI[1/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*Sqrt[z/ 3]*Exp[2*Pi*I/ 3]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]] |
Failure | Failure | Skip | Fail
Complex[-2.8337652800788247, 0.30394618618023783] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} |
| 9.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\sqrt{z/3}e^{2\pi i/3}\HankelH{1}{1/3}@{\zeta e^{\pi i/2}} = \tfrac{1}{2}\sqrt{z/3}e^{\pi i/3}\HankelH{1}{-1/3}@{\zeta e^{\pi i/2}}} | (1)/(2)*sqrt(z/ 3)*exp(2*Pi*I/ 3)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))=(1)/(2)*sqrt(z/ 3)*exp(Pi*I/ 3)*HankelH1(- 1/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2)) |
Divide[1,2]*Sqrt[z/ 3]*Exp[2*Pi*I/ 3]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]=Divide[1,2]*Sqrt[z/ 3]*Exp[Pi*I/ 3]*HankelH1[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]] |
Successful | Failure | - | Successful |
| 9.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\sqrt{z/3}e^{\pi i/3}\HankelH{1}{-1/3}@{\zeta e^{\pi i/2}} = \tfrac{1}{2}\sqrt{z/3}e^{-2\pi i/3}\HankelH{2}{1/3}@{\zeta e^{-\pi i/2}}} | (1)/(2)*sqrt(z/ 3)*exp(Pi*I/ 3)*HankelH1(- 1/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))=(1)/(2)*sqrt(z/ 3)*exp(- 2*Pi*I/ 3)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2)) |
Divide[1,2]*Sqrt[z/ 3]*Exp[Pi*I/ 3]*HankelH1[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]=Divide[1,2]*Sqrt[z/ 3]*Exp[- 2*Pi*I/ 3]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]] |
Failure | Failure | Skip | Fail
Complex[2.8337652800788256, -0.3039461861802379] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.8337652800788247, -0.3039461861802372] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\sqrt{z/3}e^{-2\pi i/3}\HankelH{2}{1/3}@{\zeta e^{-\pi i/2}} = \tfrac{1}{2}\sqrt{z/3}e^{-\pi i/3}\HankelH{2}{-1/3}@{\zeta e^{-\pi i/2}}} | (1)/(2)*sqrt(z/ 3)*exp(- 2*Pi*I/ 3)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))=(1)/(2)*sqrt(z/ 3)*exp(- Pi*I/ 3)*HankelH2(- 1/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2)) |
Divide[1,2]*Sqrt[z/ 3]*Exp[- 2*Pi*I/ 3]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]=Divide[1,2]*Sqrt[z/ 3]*Exp[- Pi*I/ 3]*HankelH2[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]] |
Successful | Failure | - | Successful |
| 9.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi'@{z} = -\pi^{-1}(z/\sqrt{3})\modBesselK{+ 2/3}@{\zeta}} | subs( temp=z, diff( AiryAi(temp), temp$(1) ) )= - (Pi)^(- 1)*(z/sqrt(3))* BesselK(+ 2/ 3, (2)/(3)*(z)^((3)/(2))) |
(D[AiryAi[temp], {temp, 1}]/.temp-> z)= - (Pi)^(- 1)*(z/Sqrt[3])* BesselK[+ 2/ 3, Divide[2,3]*(z)^(Divide[3,2])] |
Failure | Failure | Fail -.7883076520+3.485863958*I <- {z = -2^(1/2)-I*2^(1/2)}-.7883076520-3.485863958*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-0.7883076520663912, 3.485863960601928] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.7883076520663912, -3.485863960601928] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi'@{z} = -\pi^{-1}(z/\sqrt{3})\modBesselK{- 2/3}@{\zeta}} | subs( temp=z, diff( AiryAi(temp), temp$(1) ) )= - (Pi)^(- 1)*(z/sqrt(3))* BesselK(- 2/ 3, (2)/(3)*(z)^((3)/(2))) |
(D[AiryAi[temp], {temp, 1}]/.temp-> z)= - (Pi)^(- 1)*(z/Sqrt[3])* BesselK[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])] |
Failure | Failure | Fail -.7883076520+3.485863958*I <- {z = -2^(1/2)-I*2^(1/2)}-.7883076520-3.485863958*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-0.7883076520663912, 3.485863960601928] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.7883076520663912, -3.485863960601928] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\pi^{-1}(z/\sqrt{3})\modBesselK{+ 2/3}@{\zeta} = (z/3)\left(\modBesselI{2/3}@{\zeta}-\modBesselI{-2/3}@{\zeta}\right)} | - (Pi)^(- 1)*(z/sqrt(3))* BesselK(+ 2/ 3, (2)/(3)*(z)^((3)/(2)))=(z/ 3)*(BesselI(2/ 3, (2)/(3)*(z)^((3)/(2)))- BesselI(- 2/ 3, (2)/(3)*(z)^((3)/(2)))) |
- (Pi)^(- 1)*(z/Sqrt[3])* BesselK[+ 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]=(z/ 3)*(BesselI[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselI[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Successful | Successful | - | - |
| 9.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\pi^{-1}(z/\sqrt{3})\modBesselK{- 2/3}@{\zeta} = (z/3)\left(\modBesselI{2/3}@{\zeta}-\modBesselI{-2/3}@{\zeta}\right)} | - (Pi)^(- 1)*(z/sqrt(3))* BesselK(- 2/ 3, (2)/(3)*(z)^((3)/(2)))=(z/ 3)*(BesselI(2/ 3, (2)/(3)*(z)^((3)/(2)))- BesselI(- 2/ 3, (2)/(3)*(z)^((3)/(2)))) |
- (Pi)^(- 1)*(z/Sqrt[3])* BesselK[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]=(z/ 3)*(BesselI[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselI[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Successful | Successful | - | - |
| 9.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z/3)\left(\modBesselI{2/3}@{\zeta}-\modBesselI{-2/3}@{\zeta}\right) = \tfrac{1}{2}(z/\sqrt{3})e^{-\pi i/6}\HankelH{1}{2/3}@{\zeta e^{\pi i/2}}} | (z/ 3)*(BesselI(2/ 3, (2)/(3)*(z)^((3)/(2)))- BesselI(- 2/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*(z/sqrt(3))* exp(- Pi*I/ 6)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2)) |
(z/ 3)*(BesselI[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselI[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*(z/Sqrt[3])* Exp[- Pi*I/ 6]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]] |
Failure | Failure | Skip | Fail
Complex[0.7883076520663918, -3.485863960601928] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} |
| 9.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}(z/\sqrt{3})e^{-\pi i/6}\HankelH{1}{2/3}@{\zeta e^{\pi i/2}} = \tfrac{1}{2}(z/\sqrt{3})e^{-5\pi i/6}\HankelH{1}{-2/3}@{\zeta e^{\pi i/2}}} | (1)/(2)*(z/sqrt(3))* exp(- Pi*I/ 6)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))=(1)/(2)*(z/sqrt(3))* exp(- 5*Pi*I/ 6)*HankelH1(- 2/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2)) |
Divide[1,2]*(z/Sqrt[3])* Exp[- Pi*I/ 6]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]=Divide[1,2]*(z/Sqrt[3])* Exp[- 5*Pi*I/ 6]*HankelH1[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]] |
Successful | Failure | - | Successful |
| 9.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}(z/\sqrt{3})e^{-5\pi i/6}\HankelH{1}{-2/3}@{\zeta e^{\pi i/2}} = \tfrac{1}{2}(z/\sqrt{3})e^{\pi i/6}\HankelH{2}{2/3}@{\zeta e^{-\pi i/2}}} | (1)/(2)*(z/sqrt(3))* exp(- 5*Pi*I/ 6)*HankelH1(- 2/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))=(1)/(2)*(z/sqrt(3))* exp(Pi*I/ 6)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2)) |
Divide[1,2]*(z/Sqrt[3])* Exp[- 5*Pi*I/ 6]*HankelH1[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]=Divide[1,2]*(z/Sqrt[3])* Exp[Pi*I/ 6]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]] |
Failure | Failure | Skip | Fail
Complex[-0.7883076520663909, 3.485863960601928] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.7883076520663926, 3.485863960601928] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}(z/\sqrt{3})e^{\pi i/6}\HankelH{2}{2/3}@{\zeta e^{-\pi i/2}} = \tfrac{1}{2}(z/\sqrt{3})e^{5\pi i/6}\HankelH{2}{-2/3}@{\zeta e^{-\pi i/2}}} | (1)/(2)*(z/sqrt(3))* exp(Pi*I/ 6)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))=(1)/(2)*(z/sqrt(3))* exp(5*Pi*I/ 6)*HankelH2(- 2/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2)) |
Divide[1,2]*(z/Sqrt[3])* Exp[Pi*I/ 6]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]=Divide[1,2]*(z/Sqrt[3])* Exp[5*Pi*I/ 6]*HankelH2[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]] |
Successful | Failure | - | Successful |
| 9.6.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi@{z} = \sqrt{z/3}\left(\modBesselI{1/3}@{\zeta}+\modBesselI{-1/3}@{\zeta}\right)} | AiryBi(z)=sqrt(z/ 3)*(BesselI(1/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselI(- 1/ 3, (2)/(3)*(z)^((3)/(2)))) |
AiryBi[z]=Sqrt[z/ 3]*(BesselI[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselI[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Failure | Failure | Fail .323091265e-1+.116725832*I <- {z = -2^(1/2)-I*2^(1/2)}.323091265e-1-.116725832*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.032309126109843156, 0.11672583064563491] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.032309126109843156, -0.11672583064563491] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{z/3}\left(\modBesselI{1/3}@{\zeta}+\modBesselI{-1/3}@{\zeta}\right) = \tfrac{1}{2}\sqrt{z/3}\left(e^{\pi i/6}\HankelH{1}{1/3}@{\zeta e^{-\pi i/2}}+e^{-\pi i/6}\HankelH{2}{1/3}@{\zeta e^{\pi i/2}}\right)} | sqrt(z/ 3)*(BesselI(1/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselI(- 1/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*sqrt(z/ 3)*(exp(Pi*I/ 6)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))+ exp(- Pi*I/ 6)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))) |
Sqrt[z/ 3]*(BesselI[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselI[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*Sqrt[z/ 3]*(Exp[Pi*I/ 6]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]+ Exp[- Pi*I/ 6]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]) |
Failure | Failure | Fail -.1681276560-1.475245556*I <- {z = -2^(1/2)-I*2^(1/2)}-.1681276560+1.475245556*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-0.16812765614504083, -1.4752455553622306] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.16812765614504083, 1.4752455553622306] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\sqrt{z/3}\left(e^{\pi i/6}\HankelH{1}{1/3}@{\zeta e^{-\pi i/2}}+e^{-\pi i/6}\HankelH{2}{1/3}@{\zeta e^{\pi i/2}}\right) = \tfrac{1}{2}\sqrt{z/3}\left(e^{-\pi i/6}\HankelH{1}{-1/3}@{\zeta e^{-\pi i/2}}+e^{\pi i/6}\HankelH{2}{-1/3}@{\zeta e^{\pi i/2}}\right)} | (1)/(2)*sqrt(z/ 3)*(exp(Pi*I/ 6)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))+ exp(- Pi*I/ 6)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2)))=(1)/(2)*sqrt(z/ 3)*(exp(- Pi*I/ 6)*HankelH1(- 1/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))+ exp(Pi*I/ 6)*HankelH2(- 1/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))) |
Divide[1,2]*Sqrt[z/ 3]*(Exp[Pi*I/ 6]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]+ Exp[- Pi*I/ 6]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]])=Divide[1,2]*Sqrt[z/ 3]*(Exp[- Pi*I/ 6]*HankelH1[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]+ Exp[Pi*I/ 6]*HankelH2[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]) |
Successful | Failure | - | Successful |
| 9.6.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi'@{z} = (z/\sqrt{3})\left(\modBesselI{2/3}@{\zeta}+\modBesselI{-2/3}@{\zeta}\right)} | subs( temp=z, diff( AiryBi(temp), temp$(1) ) )=(z/sqrt(3))*(BesselI(2/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselI(- 2/ 3, (2)/(3)*(z)^((3)/(2)))) |
(D[AiryBi[temp], {temp, 1}]/.temp-> z)=(z/Sqrt[3])*(BesselI[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselI[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Failure | Failure | Fail .181539689+.267445042e-1*I <- {z = -2^(1/2)-I*2^(1/2)}.181539689-.267445042e-1*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.18153969005752768, 0.026744504839266825] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.18153969005752768, -0.026744504839266825] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z/\sqrt{3})\left(\modBesselI{2/3}@{\zeta}+\modBesselI{-2/3}@{\zeta}\right) = \tfrac{1}{2}(z/\sqrt{3})\left(e^{\pi i/3}\HankelH{1}{2/3}@{\zeta e^{-\pi i/2}}+e^{-\pi i/3}\HankelH{2}{2/3}@{\zeta e^{\pi i/2}}\right)} | (z/sqrt(3))*(BesselI(2/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselI(- 2/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*(z/sqrt(3))*(exp(Pi*I/ 3)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))+ exp(- Pi*I/ 3)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))) |
(z/Sqrt[3])*(BesselI[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselI[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*(z/Sqrt[3])*(Exp[Pi*I/ 3]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]+ Exp[- Pi*I/ 3]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]) |
Failure | Failure | Fail 1.652162135+.3807815744*I <- {z = -2^(1/2)-I*2^(1/2)}1.652162135-.3807815744*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[1.6521621352721998, 0.3807815736135619] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.6521621352721998, -0.3807815736135619] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}(z/\sqrt{3})\left(e^{\pi i/3}\HankelH{1}{2/3}@{\zeta e^{-\pi i/2}}+e^{-\pi i/3}\HankelH{2}{2/3}@{\zeta e^{\pi i/2}}\right) = \tfrac{1}{2}(z/\sqrt{3})\left(e^{-\pi i/3}\HankelH{1}{-2/3}@{\zeta e^{-\pi i/2}}+e^{\pi i/3}\HankelH{2}{-2/3}@{\zeta e^{\pi i/2}}\right)} | (1)/(2)*(z/sqrt(3))*(exp(Pi*I/ 3)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))+ exp(- Pi*I/ 3)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2)))=(1)/(2)*(z/sqrt(3))*(exp(- Pi*I/ 3)*HankelH1(- 2/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))+ exp(Pi*I/ 3)*HankelH2(- 2/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))) |
Divide[1,2]*(z/Sqrt[3])*(Exp[Pi*I/ 3]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]+ Exp[- Pi*I/ 3]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]])=Divide[1,2]*(z/Sqrt[3])*(Exp[- Pi*I/ 3]*HankelH1[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]+ Exp[Pi*I/ 3]*HankelH2[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]) |
Successful | Failure | - | Successful |
| 9.6.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{-z} = (\sqrt{z}/3)\left(\BesselJ{1/3}@{\zeta}+\BesselJ{-1/3}@{\zeta}\right)} | AiryAi(- z)=(sqrt(z)/ 3)*(BesselJ(1/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselJ(- 1/ 3, (2)/(3)*(z)^((3)/(2)))) |
AiryAi[- z]=(Sqrt[z]/ 3)*(BesselJ[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselJ[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Failure | Failure | Fail -.5274645816-.7652257224e-1*I <- {z = -2^(1/2)-I*2^(1/2)}-.5274645816+.7652257224e-1*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-0.5274645818155765, -0.0765225723412053] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.5274645818155765, 0.0765225723412053] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\sqrt{z}/3)\left(\BesselJ{1/3}@{\zeta}+\BesselJ{-1/3}@{\zeta}\right) = \tfrac{1}{2}\sqrt{z/3}\left(e^{\pi i/6}\HankelH{1}{1/3}@{\zeta}+e^{-\pi i/6}\HankelH{2}{1/3}@{\zeta}\right)} | (sqrt(z)/ 3)*(BesselJ(1/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselJ(- 1/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*sqrt(z/ 3)*(exp(Pi*I/ 6)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(- Pi*I/ 6)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2)))) |
(Sqrt[z]/ 3)*(BesselJ[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselJ[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*Sqrt[z/ 3]*(Exp[Pi*I/ 6]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- Pi*I/ 6]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Successful | Failure | - | Successful |
| 9.6.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\sqrt{z/3}\left(e^{\pi i/6}\HankelH{1}{1/3}@{\zeta}+e^{-\pi i/6}\HankelH{2}{1/3}@{\zeta}\right) = \tfrac{1}{2}\sqrt{z/3}\left(e^{-\pi i/6}\HankelH{1}{-1/3}@{\zeta}+e^{\pi i/6}\HankelH{2}{-1/3}@{\zeta}\right)} | (1)/(2)*sqrt(z/ 3)*(exp(Pi*I/ 6)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(- Pi*I/ 6)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*sqrt(z/ 3)*(exp(- Pi*I/ 6)*HankelH1(- 1/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(Pi*I/ 6)*HankelH2(- 1/ 3, (2)/(3)*(z)^((3)/(2)))) |
Divide[1,2]*Sqrt[z/ 3]*(Exp[Pi*I/ 6]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- Pi*I/ 6]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*Sqrt[z/ 3]*(Exp[- Pi*I/ 6]*HankelH1[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[Pi*I/ 6]*HankelH2[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Successful | Successful | - | - |
| 9.6.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi'@{-z} = (z/3)\left(\BesselJ{2/3}@{\zeta}-\BesselJ{-2/3}@{\zeta}\right)} | subs( temp=- z, diff( AiryAi(temp), temp$(1) ) )=(z/ 3)*(BesselJ(2/ 3, (2)/(3)*(z)^((3)/(2)))- BesselJ(- 2/ 3, (2)/(3)*(z)^((3)/(2)))) |
(D[AiryAi[temp], {temp, 1}]/.temp-> - z)=(z/ 3)*(BesselJ[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselJ[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Failure | Failure | Fail -.6239178317-.1120108402*I <- {z = -2^(1/2)-I*2^(1/2)}-.6239178317+.1120108402*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-0.6239178317433629, -0.1120108405877985] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.6239178317433629, 0.1120108405877985] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z/3)\left(\BesselJ{2/3}@{\zeta}-\BesselJ{-2/3}@{\zeta}\right) = \tfrac{1}{2}(z/\sqrt{3})\left(e^{-\pi i/6}\HankelH{1}{2/3}@{\zeta}+e^{\pi i/6}\HankelH{2}{2/3}@{\zeta}\right)} | (z/ 3)*(BesselJ(2/ 3, (2)/(3)*(z)^((3)/(2)))- BesselJ(- 2/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*(z/sqrt(3))*(exp(- Pi*I/ 6)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(Pi*I/ 6)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2)))) |
(z/ 3)*(BesselJ[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselJ[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*(z/Sqrt[3])*(Exp[- Pi*I/ 6]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[Pi*I/ 6]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Successful | Failure | - | Successful |
| 9.6.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}(z/\sqrt{3})\left(e^{-\pi i/6}\HankelH{1}{2/3}@{\zeta}+e^{\pi i/6}\HankelH{2}{2/3}@{\zeta}\right) = \tfrac{1}{2}(z/\sqrt{3})\left(e^{-5\pi i/6}\HankelH{1}{-2/3}@{\zeta}+e^{5\pi i/6}\HankelH{2}{-2/3}@{\zeta}\right)} | (1)/(2)*(z/sqrt(3))*(exp(- Pi*I/ 6)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(Pi*I/ 6)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*(z/sqrt(3))*(exp(- 5*Pi*I/ 6)*HankelH1(- 2/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(5*Pi*I/ 6)*HankelH2(- 2/ 3, (2)/(3)*(z)^((3)/(2)))) |
Divide[1,2]*(z/Sqrt[3])*(Exp[- Pi*I/ 6]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[Pi*I/ 6]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*(z/Sqrt[3])*(Exp[- 5*Pi*I/ 6]*HankelH1[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[5*Pi*I/ 6]*HankelH2[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Successful | Successful | - | - |
| 9.6.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi@{-z} = \sqrt{z/3}\left(\BesselJ{-1/3}@{\zeta}-\BesselJ{1/3}@{\zeta}\right)} | AiryBi(- z)=sqrt(z/ 3)*(BesselJ(- 1/ 3, (2)/(3)*(z)^((3)/(2)))- BesselJ(1/ 3, (2)/(3)*(z)^((3)/(2)))) |
AiryBi[- z]=Sqrt[z/ 3]*(BesselJ[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselJ[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Failure | Failure | Fail .4111747943+1.355498750*I <- {z = -2^(1/2)-I*2^(1/2)}.4111747943-1.355498750*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.41117479327057227, 1.355498750084894] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.41117479327057227, -1.355498750084894] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{z/3}\left(\BesselJ{-1/3}@{\zeta}-\BesselJ{1/3}@{\zeta}\right) = \tfrac{1}{2}\sqrt{z/3}\left(e^{2\pi i/3}\HankelH{1}{1/3}@{\zeta}+e^{-2\pi i/3}\HankelH{2}{1/3}@{\zeta}\right)} | sqrt(z/ 3)*(BesselJ(- 1/ 3, (2)/(3)*(z)^((3)/(2)))- BesselJ(1/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*sqrt(z/ 3)*(exp(2*Pi*I/ 3)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(- 2*Pi*I/ 3)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2)))) |
Sqrt[z/ 3]*(BesselJ[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselJ[1/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*Sqrt[z/ 3]*(Exp[2*Pi*I/ 3]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- 2*Pi*I/ 3]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Successful | Failure | - | Successful |
| 9.6.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\sqrt{z/3}\left(e^{2\pi i/3}\HankelH{1}{1/3}@{\zeta}+e^{-2\pi i/3}\HankelH{2}{1/3}@{\zeta}\right) = \tfrac{1}{2}\sqrt{z/3}\left(e^{\pi i/3}\HankelH{1}{-1/3}@{\zeta}+e^{-\pi i/3}\HankelH{2}{-1/3}@{\zeta}\right)} | (1)/(2)*sqrt(z/ 3)*(exp(2*Pi*I/ 3)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(- 2*Pi*I/ 3)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*sqrt(z/ 3)*(exp(Pi*I/ 3)*HankelH1(- 1/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(- Pi*I/ 3)*HankelH2(- 1/ 3, (2)/(3)*(z)^((3)/(2)))) |
Divide[1,2]*Sqrt[z/ 3]*(Exp[2*Pi*I/ 3]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- 2*Pi*I/ 3]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*Sqrt[z/ 3]*(Exp[Pi*I/ 3]*HankelH1[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- Pi*I/ 3]*HankelH2[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Successful | Successful | - | - |
| 9.6.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi'@{-z} = (z/\sqrt{3})\left(\BesselJ{-2/3}@{\zeta}+\BesselJ{2/3}@{\zeta}\right)} | subs( temp=- z, diff( AiryBi(temp), temp$(1) ) )=(z/sqrt(3))*(BesselJ(- 2/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselJ(2/ 3, (2)/(3)*(z)^((3)/(2)))) |
(D[AiryBi[temp], {temp, 1}]/.temp-> - z)=(z/Sqrt[3])*(BesselJ[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselJ[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Failure | Failure | Fail -1.338452844+1.884861589*I <- {z = -2^(1/2)-I*2^(1/2)}-1.338452844-1.884861589*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-1.338452844987923, 1.884861589266007] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.338452844987923, -1.884861589266007] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z/\sqrt{3})\left(\BesselJ{-2/3}@{\zeta}+\BesselJ{2/3}@{\zeta}\right) = \tfrac{1}{2}(z/\sqrt{3})\left(e^{\pi i/3}\HankelH{1}{2/3}@{\zeta}+e^{-\pi i/3}\HankelH{2}{2/3}@{\zeta}\right)} | (z/sqrt(3))*(BesselJ(- 2/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselJ(2/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*(z/sqrt(3))*(exp(Pi*I/ 3)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(- Pi*I/ 3)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2)))) |
(z/Sqrt[3])*(BesselJ[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselJ[2/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*(z/Sqrt[3])*(Exp[Pi*I/ 3]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- Pi*I/ 3]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Successful | Failure | - | Successful |
| 9.6.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}(z/\sqrt{3})\left(e^{\pi i/3}\HankelH{1}{2/3}@{\zeta}+e^{-\pi i/3}\HankelH{2}{2/3}@{\zeta}\right) = \tfrac{1}{2}(z/\sqrt{3})\left(e^{-\pi i/3}\HankelH{1}{-2/3}@{\zeta}+e^{\pi i/3}\HankelH{2}{-2/3}@{\zeta}\right)} | (1)/(2)*(z/sqrt(3))*(exp(Pi*I/ 3)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(- Pi*I/ 3)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*(z/sqrt(3))*(exp(- Pi*I/ 3)*HankelH1(- 2/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(Pi*I/ 3)*HankelH2(- 2/ 3, (2)/(3)*(z)^((3)/(2)))) |
Divide[1,2]*(z/Sqrt[3])*(Exp[Pi*I/ 3]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- Pi*I/ 3]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*(z/Sqrt[3])*(Exp[- Pi*I/ 3]*HankelH1[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[Pi*I/ 3]*HankelH2[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]) |
Successful | Successful | - | - |
| 9.6.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{+ 1/3}@{\zeta} = \tfrac{1}{2}\sqrt{3/z}\left(\sqrt{3}\AiryAi@{-z}-\AiryBi@{-z}\right)} | BesselJ(+ 1/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*sqrt(3/ z)*(sqrt(3)*AiryAi(- z)- AiryBi(- z)) |
BesselJ[+ 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*Sqrt[3/ z]*(Sqrt[3]*AiryAi[- z]- AiryBi[- z]) |
Failure | Failure | Fail -.5314179186+1.098214195*I <- {z = -2^(1/2)-I*2^(1/2)}-.5314179186-1.098214195*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-0.531417918807772, 1.09821419470116] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.531417918807772, -1.09821419470116] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{- 1/3}@{\zeta} = \tfrac{1}{2}\sqrt{3/z}\left(\sqrt{3}\AiryAi@{-z}+\AiryBi@{-z}\right)} | BesselJ(- 1/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*sqrt(3/ z)*(sqrt(3)*AiryAi(- z)+ AiryBi(- z)) |
BesselJ[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*Sqrt[3/ z]*(Sqrt[3]*AiryAi[- z]+ AiryBi[- z]) |
Failure | Failure | Fail .8096382420-.23450870e-2*I <- {z = -2^(1/2)-I*2^(1/2)}.8096382420+.23450870e-2*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.8096382422763857, -0.0023450862884800416] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.8096382422763857, 0.0023450862884800416] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{+ 2/3}@{\zeta} = \tfrac{1}{2}(\sqrt{3}/z)\left(+\sqrt{3}\AiryAi'@{-z}+\AiryBi'@{-z}\right)} | BesselJ(+ 2/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*(sqrt(3)/ z)*(+sqrt(3)*subs( temp=- z, diff( AiryAi(temp), temp$(1) ) )+ subs( temp=- z, diff( AiryBi(temp), temp$(1) ) )) |
BesselJ[+ 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*(Sqrt[3]/ z)*(+Sqrt[3]*(D[AiryAi[temp], {temp, 1}]/.temp-> - z)+ (D[AiryBi[temp], {temp, 1}]/.temp-> - z)) |
Failure | Failure | Fail -.2229822889+1.258414134*I <- {z = -2^(1/2)-I*2^(1/2)}-.2229822889-1.258414134*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-0.22298228919670726, 1.2584141341459216] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.22298228919670726, -1.2584141341459216] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{- 2/3}@{\zeta} = \tfrac{1}{2}(\sqrt{3}/z)\left(-\sqrt{3}\AiryAi'@{-z}+\AiryBi'@{-z}\right)} | BesselJ(- 2/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*(sqrt(3)/ z)*(-sqrt(3)*subs( temp=- z, diff( AiryAi(temp), temp$(1) ) )+ subs( temp=- z, diff( AiryBi(temp), temp$(1) ) )) |
BesselJ[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*(Sqrt[3]/ z)*(-Sqrt[3]*(D[AiryAi[temp], {temp, 1}]/.temp-> - z)+ (D[AiryBi[temp], {temp, 1}]/.temp-> - z)) |
Failure | Failure | Fail .5575879430+.7154547765*I <- {z = -2^(1/2)-I*2^(1/2)}.5575879430-.7154547765*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.5575879428157583, 0.7154547769715692] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.5575879428157583, -0.7154547769715692] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{+ 1/3}@{\zeta} = \tfrac{1}{2}\sqrt{3/z}\left(-\sqrt{3}\AiryAi@{z}+\AiryBi@{z}\right)} | BesselI(+ 1/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*sqrt(3/ z)*(-sqrt(3)*AiryAi(z)+ AiryBi(z)) |
BesselI[+ 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*Sqrt[3/ z]*(-Sqrt[3]*AiryAi[z]+ AiryBi[z]) |
Failure | Failure | Fail 1.506527799+2.607865458*I <- {z = -2^(1/2)-I*2^(1/2)}1.506527799-2.607865458*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[1.5065278006053275, 2.6078654586738588] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.5065278006053275, -2.6078654586738588] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{- 1/3}@{\zeta} = \tfrac{1}{2}\sqrt{3/z}\left(+\sqrt{3}\AiryAi@{z}+\AiryBi@{z}\right)} | BesselI(- 1/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*sqrt(3/ z)*(+sqrt(3)*AiryAi(z)+ AiryBi(z)) |
BesselI[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*Sqrt[3/ z]*(+Sqrt[3]*AiryAi[z]+ AiryBi[z]) |
Failure | Failure | Fail -1.389593520-2.699131954*I <- {z = -2^(1/2)-I*2^(1/2)}-1.389593520+2.699131954*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-1.3895935221249858, -2.6991319545588484] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.3895935221249858, 2.6991319545588484] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{+ 2/3}@{\zeta} = \tfrac{1}{2}(\sqrt{3}/z)\left(+\sqrt{3}\AiryAi'@{z}+\AiryBi'@{z}\right)} | BesselI(+ 2/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*(sqrt(3)/ z)*(+sqrt(3)*subs( temp=z, diff( AiryAi(temp), temp$(1) ) )+ subs( temp=z, diff( AiryBi(temp), temp$(1) ) )) |
BesselI[+ 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*(Sqrt[3]/ z)*(+Sqrt[3]*(D[AiryAi[temp], {temp, 1}]/.temp-> z)+ (D[AiryBi[temp], {temp, 1}]/.temp-> z)) |
Failure | Failure | Fail 1.494369018+2.219325646*I <- {z = -2^(1/2)-I*2^(1/2)}1.494369018-2.219325646*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[1.4943690186714658, 2.219325646151564] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.4943690186714658, -2.219325646151564] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{- 2/3}@{\zeta} = \tfrac{1}{2}(\sqrt{3}/z)\left(-\sqrt{3}\AiryAi'@{z}+\AiryBi'@{z}\right)} | BesselI(- 2/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*(sqrt(3)/ z)*(-sqrt(3)*subs( temp=z, diff( AiryAi(temp), temp$(1) ) )+ subs( temp=z, diff( AiryBi(temp), temp$(1) ) )) |
BesselI[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*(Sqrt[3]/ z)*(-Sqrt[3]*(D[AiryAi[temp], {temp, 1}]/.temp-> z)+ (D[AiryBi[temp], {temp, 1}]/.temp-> z)) |
Failure | Failure | Fail -1.366821518-2.314117950*I <- {z = -2^(1/2)-I*2^(1/2)}-1.366821518+2.314117950*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-1.366821518925578, -2.3141179507576517] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.366821518925578, 2.3141179507576517] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{+ 1/3}@{\zeta} = \pi\sqrt{3/z}\AiryAi@{z}} | BesselK(+ 1/ 3, (2)/(3)*(z)^((3)/(2)))= Pi*sqrt(3/ z)*AiryAi(z) |
BesselK[+ 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Pi*Sqrt[3/ z]*AiryAi[z] |
Failure | Failure | Fail -5.252983010-9.625828533*I <- {z = -2^(1/2)-I*2^(1/2)}-5.252983010+9.625828533*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-5.252983013913404, -9.625828534114124] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.252983013913404, 9.625828534114124] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{- 1/3}@{\zeta} = \pi\sqrt{3/z}\AiryAi@{z}} | BesselK(- 1/ 3, (2)/(3)*(z)^((3)/(2)))= Pi*sqrt(3/ z)*AiryAi(z) |
BesselK[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Pi*Sqrt[3/ z]*AiryAi[z] |
Failure | Failure | Fail -5.252983010-9.625828533*I <- {z = -2^(1/2)-I*2^(1/2)}-5.252983010+9.625828533*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-5.252983013913404, -9.625828534114124] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.252983013913404, 9.625828534114124] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{+ 2/3}@{\zeta} = -\pi(\sqrt{3}/z)\AiryAi'@{z}} | BesselK(+ 2/ 3, (2)/(3)*(z)^((3)/(2)))= - Pi*(sqrt(3)/ z)* subs( temp=z, diff( AiryAi(temp), temp$(1) ) ) |
BesselK[+ 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]= - Pi*(Sqrt[3]/ z)* (D[AiryAi[temp], {temp, 1}]/.temp-> z) |
Failure | Failure | Fail -5.189625577-8.222757114*I <- {z = -2^(1/2)-I*2^(1/2)}-5.189625577+8.222757114*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-5.189625578046477, -8.222757113865619] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.189625578046477, 8.222757113865619] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{- 2/3}@{\zeta} = -\pi(\sqrt{3}/z)\AiryAi'@{z}} | BesselK(- 2/ 3, (2)/(3)*(z)^((3)/(2)))= - Pi*(sqrt(3)/ z)* subs( temp=z, diff( AiryAi(temp), temp$(1) ) ) |
BesselK[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]= - Pi*(Sqrt[3]/ z)* (D[AiryAi[temp], {temp, 1}]/.temp-> z) |
Failure | Failure | Fail -5.189625577-8.222757114*I <- {z = -2^(1/2)-I*2^(1/2)}-5.189625577+8.222757114*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-5.189625578046477, -8.222757113865619] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.189625578046477, 8.222757113865619] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{1/3}@{\zeta} = e^{-\pi i/3}\HankelH{1}{-1/3}@{\zeta}} | HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2)))= exp(- Pi*I/ 3)*HankelH1(- 1/ 3, (2)/(3)*(z)^((3)/(2))) |
HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[- Pi*I/ 3]*HankelH1[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])] |
Successful | Successful | - | - |
| 9.6.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\pi i/3}\HankelH{1}{-1/3}@{\zeta} = e^{-\pi i/6}\sqrt{3/z}\left(\AiryAi@{-z}-i\AiryBi@{-z}\right)} | exp(- Pi*I/ 3)*HankelH1(- 1/ 3, (2)/(3)*(z)^((3)/(2)))= exp(- Pi*I/ 6)*sqrt(3/ z)*(AiryAi(- z)- I*AiryBi(- z)) |
Exp[- Pi*I/ 3]*HankelH1[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[- Pi*I/ 6]*Sqrt[3/ z]*(AiryAi[- z]- I*AiryBi[- z]) |
Failure | Failure | Fail -1.168180054-.1434897976*I <- {z = -2^(1/2)-I*2^(1/2)}.1053442159-2.339918189*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-1.1681800521462087, -0.14348979802367162] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.10534421453066467, -2.3399181874259916] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{2/3}@{\zeta} = e^{-2\pi i/3}\HankelH{1}{-2/3}@{\zeta}} | HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2)))= exp(- 2*Pi*I/ 3)*HankelH1(- 2/ 3, (2)/(3)*(z)^((3)/(2))) |
HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[- 2*Pi*I/ 3]*HankelH1[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])] |
Successful | Successful | - | - |
| 9.6.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-2\pi i/3}\HankelH{1}{-2/3}@{\zeta} = e^{\pi i/6}(\sqrt{3}/z)\left(\AiryAi'@{-z}-i\AiryBi'@{-z}\right)} | exp(- 2*Pi*I/ 3)*HankelH1(- 2/ 3, (2)/(3)*(z)^((3)/(2)))= exp(Pi*I/ 6)*(sqrt(3)/ z)*(subs( temp=- z, diff( AiryAi(temp), temp$(1) ) )- I*subs( temp=- z, diff( AiryBi(temp), temp$(1) ) )) |
Exp[- 2*Pi*I/ 3]*HankelH1[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[Pi*I/ 6]*(Sqrt[3]/ z)*((D[AiryAi[temp], {temp, 1}]/.temp-> - z)- I*(D[AiryBi[temp], {temp, 1}]/.temp-> - z)) |
Failure | Failure | Fail 1.329699466+.7433059206*I <- {z = -2^(1/2)-I*2^(1/2)}-1.775664044-1.773522348*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[1.3296994660595483, 0.7433059210750237] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.775664044452963, -1.7735223472168191] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{1/3}@{\zeta} = e^{\pi i/3}\HankelH{2}{-1/3}@{\zeta}} | HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2)))= exp(Pi*I/ 3)*HankelH2(- 1/ 3, (2)/(3)*(z)^((3)/(2))) |
HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[Pi*I/ 3]*HankelH2[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])] |
Successful | Successful | - | - |
| 9.6.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{\pi i/3}\HankelH{2}{-1/3}@{\zeta} = e^{\pi i/6}\sqrt{3/z}\left(\AiryAi@{-z}+i\AiryBi@{-z}\right)} | exp(Pi*I/ 3)*HankelH2(- 1/ 3, (2)/(3)*(z)^((3)/(2)))= exp(Pi*I/ 6)*sqrt(3/ z)*(AiryAi(- z)+ I*AiryBi(- z)) |
Exp[Pi*I/ 3]*HankelH2[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[Pi*I/ 6]*Sqrt[3/ z]*(AiryAi[- z]+ I*AiryBi[- z]) |
Failure | Failure | Fail .1053442159+2.339918189*I <- {z = -2^(1/2)-I*2^(1/2)}-1.168180054+.1434897976*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.10534421453066467, 2.3399181874259916] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.1681800521462087, 0.14348979802367162] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{2/3}@{\zeta} = e^{2\pi i/3}\HankelH{2}{-2/3}@{\zeta}} | HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2)))= exp(2*Pi*I/ 3)*HankelH2(- 2/ 3, (2)/(3)*(z)^((3)/(2))) |
HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[2*Pi*I/ 3]*HankelH2[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])] |
Successful | Successful | - | - |
| 9.6.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{2\pi i/3}\HankelH{2}{-2/3}@{\zeta} = e^{-\pi i/6}(\sqrt{3}/z)\left(\AiryAi'@{-z}+i\AiryBi'@{-z}\right)} | exp(2*Pi*I/ 3)*HankelH2(- 2/ 3, (2)/(3)*(z)^((3)/(2)))= exp(- Pi*I/ 6)*(sqrt(3)/ z)*(subs( temp=- z, diff( AiryAi(temp), temp$(1) ) )+ I*subs( temp=- z, diff( AiryBi(temp), temp$(1) ) )) |
Exp[2*Pi*I/ 3]*HankelH2[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[- Pi*I/ 6]*(Sqrt[3]/ z)*((D[AiryAi[temp], {temp, 1}]/.temp-> - z)+ I*(D[AiryBi[temp], {temp, 1}]/.temp-> - z)) |
Failure | Failure | Fail -1.775664044+1.773522348*I <- {z = -2^(1/2)-I*2^(1/2)}1.329699466-.7433059206*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-1.775664044452963, 1.7735223472168191] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.3296994660595483, -0.7433059210750237] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi'@{z} = -\tfrac{1}{2}\pi^{-1/2}z^{1/4}\WhittakerconfhyperW{0}{2/3}@{2\zeta}} | subs( temp=z, diff( AiryAi(temp), temp$(1) ) )= -(1)/(2)*(Pi)^(- 1/ 2)* (z)^(1/ 4)* WhittakerW(0, 2/ 3, 2*(2)/(3)*(z)^((3)/(2))) |
(D[AiryAi[temp], {temp, 1}]/.temp-> z)= -Divide[1,2]*(Pi)^(- 1/ 2)* (z)^(1/ 4)* WhittakerW[0, 2/ 3, 2*Divide[2,3]*(z)^(Divide[3,2])] |
Failure | Failure | Fail .89148347e-2-.60513229e-1*I <- {z = -2^(1/2)-I*2^(1/2)}.89148347e-2+.60513229e-1*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.008914834946421868, -0.06051323001917441] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.008914834946421868, 0.06051323001917441] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}\pi^{-1/2}z^{1/4}\WhittakerconfhyperW{0}{2/3}@{2\zeta} = -3^{1/6}\pi^{-1/2}\zeta^{4/3}e^{-\zeta}\KummerconfhyperU@{\tfrac{7}{6}}{\tfrac{7}{3}}{2\zeta}} | -(1)/(2)*(Pi)^(- 1/ 2)* (z)^(1/ 4)* WhittakerW(0, 2/ 3, 2*(2)/(3)*(z)^((3)/(2)))= - (3)^(1/ 6)* (Pi)^(- 1/ 2)*(2)/(3)*((z)^((3)/(2)))^(4/ 3)* exp(-(2)/(3)*(z)^((3)/(2)))*KummerU((7)/(6), (7)/(3), 2*(2)/(3)*(z)^((3)/(2))) |
-Divide[1,2]*(Pi)^(- 1/ 2)* (z)^(1/ 4)* WhittakerW[0, 2/ 3, 2*Divide[2,3]*(z)^(Divide[3,2])]= - (3)^(1/ 6)* (Pi)^(- 1/ 2)*Divide[2,3]*((z)^(Divide[3,2]))^(4/ 3)* Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricU[Divide[7,6], Divide[7,3], 2*Divide[2,3]*(z)^(Divide[3,2])] |
Failure | Failure | Fail -.316154866e-3-.241774161e-1*I <- {z = 2^(1/2)+I*2^(1/2)}-.316154866e-3+.241774161e-1*I <- {z = 2^(1/2)-I*2^(1/2)}1.587390115+1.153455370*I <- {z = -2^(1/2)-I*2^(1/2)}1.587390115-1.153455370*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-3.1615464995420756*^-4, -0.024177416299250604] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.1615464995420756*^-4, 0.024177416299250604] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.587390116444673, 1.153455375076458] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.587390116444673, -1.153455375076458] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi@{z} = \frac{1}{2^{1/3}\EulerGamma@{\tfrac{2}{3}}}z^{-1/4}\WhittakerconfhyperM{0}{-1/3}@{2\zeta}+\frac{3}{2^{5/3}\EulerGamma@{\tfrac{1}{3}}}z^{-1/4}\WhittakerconfhyperM{0}{1/3}@{2\zeta}} | AiryBi(z)=(1)/((2)^(1/ 3)* GAMMA((2)/(3)))*(z)^(- 1/ 4)* WhittakerM(0, - 1/ 3, 2*(2)/(3)*(z)^((3)/(2)))+(3)/((2)^(5/ 3)* GAMMA((1)/(3)))*(z)^(- 1/ 4)* WhittakerM(0, 1/ 3, 2*(2)/(3)*(z)^((3)/(2))) |
AiryBi[z]=Divide[1,(2)^(1/ 3)* Gamma[Divide[2,3]]]*(z)^(- 1/ 4)* WhittakerM[0, - 1/ 3, 2*Divide[2,3]*(z)^(Divide[3,2])]+Divide[3,(2)^(5/ 3)* Gamma[Divide[1,3]]]*(z)^(- 1/ 4)* WhittakerM[0, 1/ 3, 2*Divide[2,3]*(z)^(Divide[3,2])] |
Failure | Failure | Fail -.3039461866-2.833765278*I <- {z = -2^(1/2)-I*2^(1/2)}-.3039461866+2.833765278*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-0.30394618618023905, -2.8337652800788256] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.30394618618023905, 2.8337652800788256] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi'@{z} = \frac{2^{1/3}}{\EulerGamma@{\tfrac{1}{3}}}z^{1/4}\WhittakerconfhyperM{0}{-2/3}@{2\zeta}+\frac{3}{2^{10/3}\EulerGamma@{\tfrac{2}{3}}}z^{1/4}\WhittakerconfhyperM{0}{2/3}@{2\zeta}} | subs( temp=z, diff( AiryBi(temp), temp$(1) ) )=((2)^(1/ 3))/(GAMMA((1)/(3)))*(z)^(1/ 4)* WhittakerM(0, - 2/ 3, 2*(2)/(3)*(z)^((3)/(2)))+(3)/((2)^(10/ 3)* GAMMA((2)/(3)))*(z)^(1/ 4)* WhittakerM(0, 2/ 3, 2*(2)/(3)*(z)^((3)/(2))) |
(D[AiryBi[temp], {temp, 1}]/.temp-> z)=Divide[(2)^(1/ 3),Gamma[Divide[1,3]]]*(z)^(1/ 4)* WhittakerM[0, - 2/ 3, 2*Divide[2,3]*(z)^(Divide[3,2])]+Divide[3,(2)^(10/ 3)* Gamma[Divide[2,3]]]*(z)^(1/ 4)* WhittakerM[0, 2/ 3, 2*Divide[2,3]*(z)^(Divide[3,2])] |
Failure | Failure | Fail 3.485863958+.7883076513*I <- {z = -2^(1/2)-I*2^(1/2)}3.485863958-.7883076513*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[3.485863960601927, 0.7883076520663903] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[3.485863960601927, -0.7883076520663903] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi@{z} = \frac{1}{3^{1/6}\EulerGamma@{\tfrac{2}{3}}}e^{-\zeta}\genhyperF{1}{1}@{\tfrac{1}{6}}{\tfrac{1}{3}}{2\zeta}+\frac{3^{5/6}}{2^{2/3}\EulerGamma@{\tfrac{1}{3}}}\zeta^{2/3}e^{-\zeta}\genhyperF{1}{1}@{\tfrac{5}{6}}{\tfrac{5}{3}}{2\zeta}} | AiryBi(z)=(1)/((3)^(1/ 6)* GAMMA((2)/(3)))*exp(-(2)/(3)*(z)^((3)/(2)))*hypergeom([(1)/(6)], [(1)/(3)], 2*(2)/(3)*(z)^((3)/(2)))+((3)^(5/ 6))/((2)^(2/ 3)* GAMMA((1)/(3)))*(2)/(3)*((z)^((3)/(2)))^(2/ 3)* exp(-(2)/(3)*(z)^((3)/(2)))*hypergeom([(5)/(6)], [(5)/(3)], 2*(2)/(3)*(z)^((3)/(2))) |
AiryBi[z]=Divide[1,(3)^(1/ 6)* Gamma[Divide[2,3]]]*Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricPFQ[{Divide[1,6]}, {Divide[1,3]}, 2*Divide[2,3]*(z)^(Divide[3,2])]+Divide[(3)^(5/ 6),(2)^(2/ 3)* Gamma[Divide[1,3]]]*Divide[2,3]*((z)^(Divide[3,2]))^(2/ 3)* Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricPFQ[{Divide[5,6]}, {Divide[5,3]}, 2*Divide[2,3]*(z)^(Divide[3,2])] |
Failure | Failure | Fail .147168161e-1+.712025224e-1*I <- {z = 2^(1/2)+I*2^(1/2)}.147168161e-1-.712025224e-1*I <- {z = 2^(1/2)-I*2^(1/2)}-1.474010305-1.772597131*I <- {z = -2^(1/2)-I*2^(1/2)}-1.474010305+1.772597131*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.014716817548916183, 0.07120252241962582] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.014716817548916183, -0.07120252241962582] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.474010305021376, -1.7725971311665962] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.474010305021376, 1.7725971311665962] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.6.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi'@{z} = \frac{3^{1/6}}{\EulerGamma@{\tfrac{1}{3}}}e^{-\zeta}\genhyperF{1}{1}@{-\tfrac{1}{6}}{-\tfrac{1}{3}}{2\zeta}+\frac{3^{7/6}}{2^{7/3}\EulerGamma@{\tfrac{2}{3}}}\zeta^{4/3}e^{-\zeta}\genhyperF{1}{1}@{\tfrac{7}{6}}{\tfrac{7}{3}}{2\zeta}} | subs( temp=z, diff( AiryBi(temp), temp$(1) ) )=((3)^(1/ 6))/(GAMMA((1)/(3)))*exp(-(2)/(3)*(z)^((3)/(2)))*hypergeom([-(1)/(6)], [-(1)/(3)], 2*(2)/(3)*(z)^((3)/(2)))+((3)^(7/ 6))/((2)^(7/ 3)* GAMMA((2)/(3)))*(2)/(3)*((z)^((3)/(2)))^(4/ 3)* exp(-(2)/(3)*(z)^((3)/(2)))*hypergeom([(7)/(6)], [(7)/(3)], 2*(2)/(3)*(z)^((3)/(2))) |
(D[AiryBi[temp], {temp, 1}]/.temp-> z)=Divide[(3)^(1/ 6),Gamma[Divide[1,3]]]*Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricPFQ[{-Divide[1,6]}, {-Divide[1,3]}, 2*Divide[2,3]*(z)^(Divide[3,2])]+Divide[(3)^(7/ 6),(2)^(7/ 3)* Gamma[Divide[2,3]]]*Divide[2,3]*((z)^(Divide[3,2]))^(4/ 3)* Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricPFQ[{Divide[7,6]}, {Divide[7,3]}, 2*Divide[2,3]*(z)^(Divide[3,2])] |
Failure | Failure | Fail .522018891e-1-.1117022869*I <- {z = 2^(1/2)+I*2^(1/2)}.522018891e-1+.1117022869*I <- {z = 2^(1/2)-I*2^(1/2)}2.583360720+2.078187022*I <- {z = -2^(1/2)-I*2^(1/2)}2.583360720-2.078187022*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.0522018904439151, -0.11170228512421254] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0522018904439151, 0.11170228512421254] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[2.5833607207543476, 2.078187024166196] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.5833607207543476, -2.078187024166196] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.7#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{x} <= \frac{e^{-\xi}}{2\sqrt{\pi}x^{1/4}}} | AiryAi(x)< =(exp(- xi))/(2*sqrt(Pi)*(x)^(1/ 4)) |
AiryAi[x]< =Divide[Exp[- \[Xi]],2*Sqrt[Pi]*(x)^(1/ 4)] |
Failure | Failure | Successful | Successful |
| 9.7#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\AiryAi'@{x}| <= \frac{x^{1/4}e^{-\xi}}{2\sqrt{\pi}}\left(1+\frac{7}{72\xi}\right)} | abs(subs( temp=x, diff( AiryAi(temp), temp$(1) ) ))< =((x)^(1/ 4)* exp(- xi))/(2*sqrt(Pi))*(1 +(7)/(72*xi)) |
Abs[D[AiryAi[temp], {temp, 1}]/.temp-> x]< =Divide[(x)^(1/ 4)* Exp[- \[Xi]],2*Sqrt[Pi]]*(1 +Divide[7,72*\[Xi]]) |
Failure | Failure | Successful | Successful |
| 9.7#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi@{x} <= \frac{\expe^{\xi}}{\sqrt{\cpi}x^{1/4}}\left(1+\left(\chi(\tfrac{7}{6})+1\right)\frac{5}{72\xi}\right)} | AiryBi(x)< =(exp(xi))/(sqrt(Pi)*(x)^(1/ 4))*(1 +(chi*((7)/(6))+ 1)*(5)/(72*xi)) |
AiryBi[x]< =Divide[Exp[\[Xi]],Sqrt[Pi]*(x)^(1/ 4)]*(1 +(\[Chi]*(Divide[7,6])+ 1)*Divide[5,72*\[Xi]]) |
Failure | Failure | Successful | Successful |
| 9.7#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi'@{x} <= \frac{x^{1/4}e^{\xi}}{\sqrt{\pi}}\left(1+\left(\frac{\cpi}{2}+1\right)\frac{7}{72\xi}\right)} | subs( temp=x, diff( AiryBi(temp), temp$(1) ) )< =((x)^(1/ 4)* exp(xi))/(sqrt(Pi))*(1 +((Pi)/(2)+ 1)*(7)/(72*xi)) |
(D[AiryBi[temp], {temp, 1}]/.temp-> x)< =Divide[(x)^(1/ 4)* Exp[\[Xi]],Sqrt[Pi]]*(1 +(Divide[Pi,2]+ 1)*Divide[7,72*\[Xi]]) |
Failure | Failure | Successful | Successful |
| 9.7.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{cases}1,&|\phase@@{z}| <= \tfrac{1}{3}\cpi,\\ \min\left(|\csc@{\phase@@{\zeta}}|,\chi(n+\sigma)+1\right),&\tfrac{1}{3}\cpi} | |
|
Error | Error | - | - |
| 9.7.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{z} = \frac{e^{-\zeta}}{2\sqrt{\pi}z^{1/4}}\left(\sum_{k=0}^{n-1}(-1)^{k}\frac{u_{k}}{\zeta^{k}}+R_{n}(z)\right)} | AiryAi(z)=(exp(-(2)/(3)*(z)^((3)/(2))))/(2*sqrt(Pi)*(z)^(1/ 4))*(sum((- 1)^(k)*(u[k])/((2)/(3)*((z)^((3)/(2)))^(k)), k = 0..n - 1)+ R[n]*(z)) |
AiryAi[z]=Divide[Exp[-Divide[2,3]*(z)^(Divide[3,2])],2*Sqrt[Pi]*(z)^(1/ 4)]*(Sum[(- 1)^(k)*Divide[Subscript[u, k],Divide[2,3]*((z)^(Divide[3,2]))^(k)], {k, 0, n - 1}]+ Subscript[R, n]*(z)) |
Failure | Failure | Skip | Skip |
| 9.7.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi'@{z} = -\frac{z^{1/4}e^{-\zeta}}{2\sqrt{\pi}}\left(\sum_{k=0}^{n-1}(-1)^{k}\frac{v_{k}}{\zeta^{k}}+S_{n}(z)\right)} | subs( temp=z, diff( AiryAi(temp), temp$(1) ) )= -((z)^(1/ 4)* exp(-(2)/(3)*(z)^((3)/(2))))/(2*sqrt(Pi))*(sum((- 1)^(k)*(v[k])/((2)/(3)*((z)^((3)/(2)))^(k)), k = 0..n - 1)+ S[n]*(z)) |
(D[AiryAi[temp], {temp, 1}]/.temp-> z)= -Divide[(z)^(1/ 4)* Exp[-Divide[2,3]*(z)^(Divide[3,2])],2*Sqrt[Pi]]*(Sum[(- 1)^(k)*Divide[Subscript[v, k],Divide[2,3]*((z)^(Divide[3,2]))^(k)], {k, 0, n - 1}]+ Subscript[S, n]*(z)) |
Failure | Failure | Skip | Skip |
| 9.7.E22 | 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 | - | - |
| 9.8.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{x} = \AirymodM@{x}\sin@@{\Airyphasetheta@{x}}} | AiryAi(x)= sqrt(AiryAi(x)^2+AiryBi(x)^2)*sin(arctan(AiryAi(x)/AiryBi(x))) |
AiryAi[x]= Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*Sin[ArcTan[Divide[AiryAi[x], AiryBi[x]]]] |
Failure | Failure | Successful | Successful |
| 9.8.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi@{x} = \AirymodM@{x}\cos@@{\Airyphasetheta@{x}}} | AiryBi(x)= sqrt(AiryAi(x)^2+AiryBi(x)^2)*cos(arctan(AiryAi(x)/AiryBi(x))) |
AiryBi[x]= Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*Cos[ArcTan[Divide[AiryAi[x], AiryBi[x]]]] |
Failure | Failure | Successful | Successful |
| 9.8.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AirymodM@{x} = \sqrt{\AiryAi^{2}@{x}+\AiryBi^{2}@{x}}} | sqrt(AiryAi(x)^2+AiryBi(x)^2)=sqrt((AiryAi(x))^(2)+ (AiryBi(x))^(2)) |
Sqrt[AiryAi[x]^2 + AiryBi[x]^2]=Sqrt[(AiryAi[x])^(2)+ (AiryBi[x])^(2)] |
Successful | Successful | - | - |
| 9.8.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Airyphasetheta@{x} = \atan@{\AiryAi@{x}/\AiryBi@{x}}} | arctan(AiryAi(x)/AiryBi(x))= arctan(AiryAi(x)/ AiryBi(x)) |
ArcTan[Divide[AiryAi[x], AiryBi[x]]]= ArcTan[AiryAi[x]/ AiryBi[x]] |
Successful | Successful | - | - |
| 9.8.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi'@{x} = \AirymodderivN@{x}\sin@@{\Airyphasederivphi@{x}}} | subs( temp=x, diff( AiryAi(temp), temp$(1) ) )= sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2)*sin(arctan(AiryAi(1, x)/AiryBi(1, x))) |
(D[AiryAi[temp], {temp, 1}]/.temp-> x)= Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2]*Sin[ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]] |
Failure | Failure | Successful | Successful |
| 9.8.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi'@{x} = \AirymodderivN@{x}\cos@@{\Airyphasederivphi@{x}}} | subs( temp=x, diff( AiryBi(temp), temp$(1) ) )= sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2)*cos(arctan(AiryAi(1, x)/AiryBi(1, x))) |
(D[AiryBi[temp], {temp, 1}]/.temp-> x)= Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2]*Cos[ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]] |
Failure | Failure | Successful | Successful |
| 9.8.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AirymodderivN@{x} = \sqrt{\AiryAi'^{2}@{x}+\AiryBi'^{2}@{x}}} | sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2)=sqrt((subs( temp=x, diff( AiryAi(temp), temp$(1) ) ))^(2)+ (subs( temp=x, diff( AiryBi(temp), temp$(1) ) ))^(2)) |
Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2]=Sqrt[((D[AiryAi[temp], {temp, 1}]/.temp-> x))^(2)+ ((D[AiryBi[temp], {temp, 1}]/.temp-> x))^(2)] |
Successful | Successful | - | - |
| 9.8.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Airyphasederivphi@{x} = \atan@{\AiryAi'@{x}/\AiryBi'@{x}}} | arctan(AiryAi(1, x)/AiryBi(1, x))= arctan(subs( temp=x, diff( AiryAi(temp), temp$(1) ) )/ subs( temp=x, diff( AiryBi(temp), temp$(1) ) )) |
ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]= ArcTan[(D[AiryAi[temp], {temp, 1}]/.temp-> x)/ (D[AiryBi[temp], {temp, 1}]/.temp-> x)] |
Successful | Successful | - | - |
| 9.8.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |x|^{1/2}\AirymodM^{2}@{x} = \tfrac{1}{2}\xi\left(\BesselJ{1/3}^{2}@{\xi}+\BesselY{1/3}^{2}@{\xi}\right)} | (abs(x))^(1/ 2)* (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)=(1)/(2)*xi*((BesselJ(1/ 3, xi))^(2)+ (BesselY(1/ 3, xi))^(2)) |
(Abs[x])^(1/ 2)* (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)=Divide[1,2]*\[Xi]*((BesselJ[1/ 3, \[Xi]])^(2)+ (BesselY[1/ 3, \[Xi]])^(2)) |
Failure | Failure | Fail 1.159089025-.4715106810e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1}15.06764807-.4715106810e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2}340.9777186-.4715106810e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3}1.159089025+.4715106810e-2*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[1.1590890245070966, -0.004715107328741586] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[15.06764807713232, -0.004715107328741586] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[340.9777188366776, -0.004715107328741586] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.1590890245070966, 0.004715107328741586] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 9.8.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |x|^{-1/2}\AirymodderivN^{2}@{x} = \tfrac{1}{2}\xi\left(\BesselJ{2/3}^{2}@{\xi}+\BesselY{2/3}^{2}@{\xi}\right)} | (abs(x))^(- 1/ 2)* (sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2)=(1)/(2)*xi*((BesselJ(2/ 3, xi))^(2)+ (BesselY(2/ 3, xi))^(2)) |
(Abs[x])^(- 1/ 2)* (Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(2)=Divide[1,2]*\[Xi]*((BesselJ[2/ 3, \[Xi]])^(2)+ (BesselY[2/ 3, \[Xi]])^(2)) |
Failure | Failure | Fail .5749530917+.6794393049e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1}11.57260149+.6794393049e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2}303.0362324+.6794393049e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3}.5749530917-.6794393049e-2*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[0.5749530907924223, 0.0067943920267909685] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[11.572601490351364, 0.0067943920267909685] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[303.0362323510325, 0.0067943920267909685] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.5749530907924223, -0.0067943920267909685] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 9.8.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Airyphasetheta@{x} = \tfrac{2}{3}\pi+\atan@{\BesselY{1/3}@{\xi}/\BesselJ{1/3}@{\xi}}} | arctan(AiryAi(x)/AiryBi(x))=(2)/(3)*Pi + arctan(BesselY(1/ 3, xi)/ BesselJ(1/ 3, xi)) |
ArcTan[Divide[AiryAi[x], AiryBi[x]]]=Divide[2,3]*Pi + ArcTan[BesselY[1/ 3, \[Xi]]/ BesselJ[1/ 3, \[Xi]]] |
Failure | Failure | Fail -2.062235934-1.435552558*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1}-2.163232204-1.435552558*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2}-2.173351447-1.435552558*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3}-2.062235934+1.435552558*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[-2.062235934109286, -1.435552557338311] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.163232204380712, -1.435552557338311] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.17335144762396, -1.435552557338311] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.062235934109286, 1.435552557338311] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 9.8.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Airyphasederivphi@{x} = \tfrac{1}{3}\pi+\atan@{\BesselY{2/3}@{\xi}/\BesselJ{2/3}@{\xi}}} | arctan(AiryAi(1, x)/AiryBi(1, x))=(1)/(3)*Pi + arctan(BesselY(2/ 3, xi)/ BesselJ(2/ 3, xi)) |
ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]=Divide[1,3]*Pi + ArcTan[BesselY[2/ 3, \[Xi]]/ BesselJ[2/ 3, \[Xi]]] |
Failure | Failure | Fail -.8340487847-1.384157839*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1}-.6779445534-1.384157839*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2}-.6655182693-1.384157839*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3}-.8340487847+1.384157839*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[-0.8340487867218234, -1.3841578383770126] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.6779445554392751, -1.3841578383770126] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.6655182713247128, -1.3841578383770126] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.8340487867218234, 1.3841578383770126] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 9.8.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AirymodM@{x}\AirymodderivN@{x}\sin@{\Airyphasetheta@{x}-\Airyphasederivphi@{x}} = \pi^{-1}} | sqrt(AiryAi(x)^2+AiryBi(x)^2)*sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2)*sin(arctan(AiryAi(x)/AiryBi(x))- arctan(AiryAi(1, x)/AiryBi(1, x)))= (Pi)^(- 1) |
Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2]*Sin[ArcTan[Divide[AiryAi[x], AiryBi[x]]]- ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]]= (Pi)^(- 1) |
Failure | Failure | Successful | Successful |
| 9.8#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AirymodM^{2}@{x}\Airyphasetheta'@{x} = -\pi^{-1}} | (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)* subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(1) ) )= - (Pi)^(- 1) |
(Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)* (D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 1}]/.temp-> x)= - (Pi)^(- 1) |
Failure | Successful | Successful | - |
| 9.8#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AirymodderivN^{2}@{x}\Airyphasederivphi'@{x} = \pi^{-1}x} | (sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2)* subs( temp=x, diff( arctan(AiryAi(1, temp)/AiryBi(1, temp)), temp$(1) ) )= (Pi)^(- 1)* x |
(Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(2)* (D[ArcTan[Divide[AiryAiPrime[temp], AiryBiPrime[temp]]], {temp, 1}]/.temp-> x)= (Pi)^(- 1)* x |
Failure | Successful | Successful | - |
| 9.8#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AirymodderivN@{x}\AirymodderivN'@{x} = x\AirymodM@{x}\AirymodM'@{x}} | sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2)*subs( temp=x, diff( sqrt(AiryAi(1, temp)^2+AiryBi(1, temp)^2), temp$(1) ) )= x*sqrt(AiryAi(x)^2+AiryBi(x)^2)*subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) ) |
Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2]*(D[Sqrt[AiryAiPrime[temp]^2 + AiryBiPrime[temp]^2], {temp, 1}]/.temp-> x)= x*Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*(D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> x) |
Successful | Successful | - | - |
| 9.8.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AirymodderivN^{2}@{x} = \AirymodM'^{2}@{x}+\AirymodM^{2}@{x}\Airyphasetheta'^{2}@{x}} | (sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2)= (subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) ))^(2)+ (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)* (subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(1) ) ))^(2) |
(Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(2)= ((D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> x))^(2)+ (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)* ((D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 1}]/.temp-> x))^(2) |
Successful | Successful | - | - |
| 9.8.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AirymodM'^{2}@{x}+\AirymodM^{2}@{x}\Airyphasetheta'^{2}@{x} = \AirymodM'^{2}(x)+\pi^{-2}\AirymodM^{-2}@{x}} | (subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) ))^(2)+ (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)* (subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(1) ) ))^(2)= (subs( temp=(x), diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) ))^(2)+ (Pi)^(- 2)* (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(- 2) |
((D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> x))^(2)+ (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)* ((D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 1}]/.temp-> x))^(2)= ((D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> (x)))^(2)+ (Pi)^(- 2)* (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(- 2) |
Failure | Successful | Successful | - |
| 9.8.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{2}\AirymodM^{2}@{x} = \AirymodderivN'^{2}@{x}+\AirymodderivN^{2}@{x}\Airyphasederivphi'^{2}@{x}} | (x)^(2)* (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)= (subs( temp=x, diff( sqrt(AiryAi(1, temp)^2+AiryBi(1, temp)^2), temp$(1) ) ))^(2)+ (sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2)* (subs( temp=x, diff( arctan(AiryAi(1, temp)/AiryBi(1, temp)), temp$(1) ) ))^(2) |
(x)^(2)* (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)= ((D[Sqrt[AiryAiPrime[temp]^2 + AiryBiPrime[temp]^2], {temp, 1}]/.temp-> x))^(2)+ (Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(2)* ((D[ArcTan[Divide[AiryAiPrime[temp], AiryBiPrime[temp]]], {temp, 1}]/.temp-> x))^(2) |
Successful | Successful | - | - |
| 9.8.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AirymodderivN'^{2}@{x}+\AirymodderivN^{2}@{x}\Airyphasederivphi'^{2}@{x} = \AirymodderivN'^{2}@{x}+\pi^{-2}x^{2}\AirymodderivN^{-2}@{x}} | (subs( temp=x, diff( sqrt(AiryAi(1, temp)^2+AiryBi(1, temp)^2), temp$(1) ) ))^(2)+ (sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2)* (subs( temp=x, diff( arctan(AiryAi(1, temp)/AiryBi(1, temp)), temp$(1) ) ))^(2)= (subs( temp=x, diff( sqrt(AiryAi(1, temp)^2+AiryBi(1, temp)^2), temp$(1) ) ))^(2)+ (Pi)^(- 2)* (x)^(2)* (sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(- 2) |
((D[Sqrt[AiryAiPrime[temp]^2 + AiryBiPrime[temp]^2], {temp, 1}]/.temp-> x))^(2)+ (Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(2)* ((D[ArcTan[Divide[AiryAiPrime[temp], AiryBiPrime[temp]]], {temp, 1}]/.temp-> x))^(2)= ((D[Sqrt[AiryAiPrime[temp]^2 + AiryBiPrime[temp]^2], {temp, 1}]/.temp-> x))^(2)+ (Pi)^(- 2)* (x)^(2)* (Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(- 2) |
Failure | Successful | Successful | - |
| 9.8.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@{\Airyphasetheta@{x}-\Airyphasederivphi@{x}} = 1/(\pi\AirymodM@{x}\AirymodM'@{x})} | tan(arctan(AiryAi(x)/AiryBi(x))- arctan(AiryAi(1, x)/AiryBi(1, x)))= 1/(Pi*sqrt(AiryAi(x)^2+AiryBi(x)^2)*subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) )) |
Tan[ArcTan[Divide[AiryAi[x], AiryBi[x]]]- ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]]= 1/(Pi*Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*(D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> x)) |
Failure | Successful | Successful | - |
| 9.8.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1/(\pi\AirymodM@{x}\AirymodM'@{x}) = -\AirymodM@{x}\Airyphasetheta'@{x}/\AirymodM'@{x}} | 1/(Pi*sqrt(AiryAi(x)^2+AiryBi(x)^2)*subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) ))= - sqrt(AiryAi(x)^2+AiryBi(x)^2)*subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(1) ) )/ subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) ) |
1/(Pi*Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*(D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> x))= - Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*(D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 1}]/.temp-> x)/ (D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> x) |
Failure | Successful | Successful | - |
| 9.8#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AirymodM''@{x} = x\AirymodM@{x}+\pi^{-2}\AirymodM^{-3}@{x}} | subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(2) ) )= x*sqrt(AiryAi(x)^2+AiryBi(x)^2)+ (Pi)^(- 2)* (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(- 3) |
(D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 2}]/.temp-> x)= x*Sqrt[AiryAi[x]^2 + AiryBi[x]^2]+ (Pi)^(- 2)* (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(- 3) |
Failure | Successful | Successful | - |
| 9.8#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AirymodM^{2}'''@{x}-4x\AirymodM^{2}'@{x}-2\AirymodM^{2}@{x} = 0} | (subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(3) ) ))^(2)- 4*x*(subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) ))^(2)- 2*(sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)= 0 |
((D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 3}]/.temp-> x))^(2)- 4*x*((D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> x))^(2)- 2*(Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)= 0 |
Failure | Failure | Fail -2.268412261 <- {x = 1}-24.26674995 <- {x = 2}157.2405245 <- {x = 3} |
Fail
-2.2684122541643257 <- {Rule[x, 1]}-24.266750191340662 <- {Rule[x, 2]}157.2404952502784 <- {Rule[x, 3]} |
| 9.8.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Airyphasetheta'^{2}@{x}+\tfrac{1}{2}(\Airyphasetheta'''@{x}/\Airyphasetheta'@{x})-\tfrac{3}{4}(\Airyphasetheta''@{x}/\Airyphasetheta'@{x})^{2} = -x} | (subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(1) ) ))^(2)+(1)/(2)*(subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(3) ) )/ subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(1) ) ))-(3)/(4)*(subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(2) ) )/ subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(1) ) ))^(2)= - x |
((D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 1}]/.temp-> x))^(2)+Divide[1,2]*((D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 3}]/.temp-> x)/ (D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 1}]/.temp-> x))-Divide[3,4]*(((D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 2}]/.temp-> x)/ (D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 1}]/.temp-> x)))^(2)= - x |
Successful | Successful | - | - |
| 9.10.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{z}^{\infty}\AiryAi@{t}\diff{t} = \pi\left(\AiryAi@{z}\ScorerGi'@{z}-\AiryAi'@{z}\ScorerGi@{z}\right)} | int(AiryAi(t), t = z..infinity)= Pi*(AiryAi(z)*subs( temp=z, diff( AiryBi(temp)*(int(AiryAi(t), t = (temp) .. infinity))+AiryAi(temp)*(int(AiryBi(t), t = 0 .. (temp))), temp$(1) ) )- subs( temp=z, diff( AiryAi(temp), temp$(1) ) )*AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))) |
Integrate[AiryAi[t], {t, z, Infinity}]= Pi*(AiryAi[z]*(D[ScorerGi[temp], {temp, 1}]/.temp-> z)- (D[AiryAi[temp], {temp, 1}]/.temp-> z)*ScorerGi[z]) |
Failure | Failure | Skip | Successful |
| 9.10.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{z}\AiryAi@{t}\diff{t} = \pi\left(\AiryAi@{z}\ScorerHi'@{z}-\AiryAi'@{z}\ScorerHi@{z}\right)} | int(AiryAi(t), t = - infinity..z)= Pi*(AiryAi(z)*subs( temp=z, diff( AiryBi(temp)*(int(AiryAi(t), t = -infinity .. (temp)))-AiryAi(temp)*(int(AiryBi(t), t = -infinity .. (temp))), temp$(1) ) )- subs( temp=z, diff( AiryAi(temp), temp$(1) ) )*AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))) |
Integrate[AiryAi[t], {t, - Infinity, z}]= Pi*(AiryAi[z]*(D[ScorerHi[temp], {temp, 1}]/.temp-> z)- (D[AiryAi[temp], {temp, 1}]/.temp-> z)*ScorerHi[z]) |
Failure | Failure | Skip | Successful |
| 9.10.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{z}\AiryBi@{t}\diff{t} = \int_{0}^{z}\AiryBi@{t}\diff{t}} | int(AiryBi(t), t = - infinity..z)= int(AiryBi(t), t = 0..z) |
Integrate[AiryBi[t], {t, - Infinity, z}]= Integrate[AiryBi[t], {t, 0, z}] |
Successful | Failure | - | Successful |
| 9.10.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pi\left(\AiryBi'@{z}\ScorerGi@{z}-\AiryBi@{z}\ScorerGi'@{z}\right)\\ = \pi\left(\AiryBi@{z}\ScorerHi'@{z}-\AiryBi'@{z}\ScorerHi@{z}\right)} | Pi*(subs( temp=z, diff( AiryBi(temp), temp$(1) ) )*AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))- AiryBi(z)*subs( temp=z, diff( AiryBi(temp)*(int(AiryAi(t), t = (temp) .. infinity))+AiryAi(temp)*(int(AiryBi(t), t = 0 .. (temp))), temp$(1) ) ))= Pi*(AiryBi(z)*subs( temp=z, diff( AiryBi(temp)*(int(AiryAi(t), t = -infinity .. (temp)))-AiryAi(temp)*(int(AiryBi(t), t = -infinity .. (temp))), temp$(1) ) )- subs( temp=z, diff( AiryBi(temp), temp$(1) ) )*AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))) |
Pi*((D[AiryBi[temp], {temp, 1}]/.temp-> z)*ScorerGi[z]- AiryBi[z]*(D[ScorerGi[temp], {temp, 1}]/.temp-> z))= Pi*(AiryBi[z]*(D[ScorerHi[temp], {temp, 1}]/.temp-> z)- (D[AiryBi[temp], {temp, 1}]/.temp-> z)*ScorerHi[z]) |
Error | Error | - | - |
| 9.10#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\AiryAi@{t}\diff{t} = \tfrac{1}{3}} | int(AiryAi(t), t = 0..infinity)=(1)/(3) |
Integrate[AiryAi[t], {t, 0, Infinity}]=Divide[1,3] |
Successful | Successful | - | - |
| 9.10#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{0}\AiryAi@{t}\diff{t} = \tfrac{2}{3}} | int(AiryAi(t), t = - infinity..0)=(2)/(3) |
Integrate[AiryAi[t], {t, - Infinity, 0}]=Divide[2,3] |
Successful | Failure | - | Successful |
| 9.10.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{0}\AiryBi@{t}\diff{t} = 0} | int(AiryBi(t), t = - infinity..0)= 0 |
Integrate[AiryBi[t], {t, - Infinity, 0}]= 0 |
Successful | Failure | - | Successful |
| 9.10.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}e^{pt}\AiryAi@{t}\diff{t} = e^{p^{3}/3}} | int(exp(p*t)*AiryAi(t), t = - infinity..infinity)= exp((p)^(3)/ 3) |
Integrate[Exp[p*t]*AiryAi[t], {t, - Infinity, Infinity}]= Exp[(p)^(3)/ 3] |
Failure | Failure | Skip | Error |
| 9.10.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-pt}\AiryAi@{t}\diff{t} = e^{-p^{3}/3}\left(\frac{1}{3}-\frac{p\genhyperF{1}{1}@{\tfrac{1}{3}}{\tfrac{4}{3}}{\tfrac{1}{3}p^{3}}}{3^{4/3}\EulerGamma@{\tfrac{4}{3}}}+\frac{p^{2}\genhyperF{1}{1}@{\tfrac{2}{3}}{\tfrac{5}{3}}{\tfrac{1}{3}p^{3}}}{3^{5/3}\EulerGamma@{\tfrac{5}{3}}}\right)} | int(exp(- p*t)*AiryAi(t), t = 0..infinity)= exp(- (p)^(3)/ 3)*((1)/(3)-(p*hypergeom([(1)/(3)], [(4)/(3)], (1)/(3)*(p)^(3)))/((3)^(4/ 3)* GAMMA((4)/(3)))+((p)^(2)* hypergeom([(2)/(3)], [(5)/(3)], (1)/(3)*(p)^(3)))/((3)^(5/ 3)* GAMMA((5)/(3)))) |
Integrate[Exp[- p*t]*AiryAi[t], {t, 0, Infinity}]= Exp[- (p)^(3)/ 3]*(Divide[1,3]-Divide[p*HypergeometricPFQ[{Divide[1,3]}, {Divide[4,3]}, Divide[1,3]*(p)^(3)],(3)^(4/ 3)* Gamma[Divide[4,3]]]+Divide[(p)^(2)* HypergeometricPFQ[{Divide[2,3]}, {Divide[5,3]}, Divide[1,3]*(p)^(3)],(3)^(5/ 3)* Gamma[Divide[5,3]]]) |
Successful | Failure | - | Successful |
| 9.10.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-pt}\AiryAi@{-t}\diff{t} = {\frac{1}{3}e^{p^{3}/3}\left(\frac{\incGamma@{\tfrac{1}{3}}{\tfrac{1}{3}p^{3}}}{\EulerGamma@{\tfrac{1}{3}}}+\frac{\incGamma@{\tfrac{2}{3}}{\tfrac{1}{3}p^{3}}}{\EulerGamma@{\tfrac{2}{3}}}\right)}} | int(exp(- p*t)*AiryAi(- t), t = 0..infinity)=(1)/(3)*exp((p)^(3)/ 3)*((GAMMA((1)/(3), (1)/(3)*(p)^(3)))/(GAMMA((1)/(3)))+(GAMMA((2)/(3), (1)/(3)*(p)^(3)))/(GAMMA((2)/(3)))) |
Integrate[Exp[- p*t]*AiryAi[- t], {t, 0, Infinity}]=Divide[1,3]*Exp[(p)^(3)/ 3]*(Divide[Gamma[Divide[1,3], Divide[1,3]*(p)^(3)],Gamma[Divide[1,3]]]+Divide[Gamma[Divide[2,3], Divide[1,3]*(p)^(3)],Gamma[Divide[2,3]]]) |
Failure | Failure | Skip | Error |
| 9.10.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-pt}\AiryBi@{-t}\diff{t} = {\frac{1}{\sqrt{3}}e^{p^{3}/3}\left(\frac{\incGamma@{\tfrac{2}{3}}{\tfrac{1}{3}p^{3}}}{\EulerGamma@{\tfrac{2}{3}}}-\frac{\incGamma@{\tfrac{1}{3}}{\tfrac{1}{3}p^{3}}}{\EulerGamma@{\tfrac{1}{3}}}\right)}} | int(exp(- p*t)*AiryBi(- t), t = 0..infinity)=(1)/(sqrt(3))*exp((p)^(3)/ 3)*((GAMMA((2)/(3), (1)/(3)*(p)^(3)))/(GAMMA((2)/(3)))-(GAMMA((1)/(3), (1)/(3)*(p)^(3)))/(GAMMA((1)/(3)))) |
Integrate[Exp[- p*t]*AiryBi[- t], {t, 0, Infinity}]=Divide[1,Sqrt[3]]*Exp[(p)^(3)/ 3]*(Divide[Gamma[Divide[2,3], Divide[1,3]*(p)^(3)],Gamma[Divide[2,3]]]-Divide[Gamma[Divide[1,3], Divide[1,3]*(p)^(3)],Gamma[Divide[1,3]]]) |
Failure | Failure | Skip | Error |
| 9.10.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{z} = \frac{3z^{5/4}e^{-(2/3)z^{3/2}}}{4\pi}\*\int_{0}^{\infty}\frac{t^{-3/4}e^{-(2/3)t^{3/2}}\AiryAi@{t}}{z^{3/2}+t^{3/2}}\diff{t}} | AiryAi(z)=(3*(z)^(5/ 4)* exp(-(2/ 3)* (z)^(3/ 2)))/(4*Pi)* int(((t)^(- 3/ 4)* exp(-(2/ 3)* (t)^(3/ 2))*AiryAi(t))/((z)^(3/ 2)+ (t)^(3/ 2)), t = 0..infinity) |
AiryAi[z]=Divide[3*(z)^(5/ 4)* Exp[-(2/ 3)* (z)^(3/ 2)],4*Pi]* Integrate[Divide[(t)^(- 3/ 4)* Exp[-(2/ 3)* (t)^(3/ 2)]*AiryAi[t],(z)^(3/ 2)+ (t)^(3/ 2)], {t, 0, Infinity}] |
Error | Failure | - | Error |
| 9.10#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{z} = \frac{z^{5/4}e^{-(2/3)z^{3/2}}}{2^{7/2}\pi}\*\int_{0}^{\infty}\frac{t^{-1/2}e^{-(2/3)t^{3/2}}\AiryAi@{t}}{z^{3/2}+t^{3/2}}\diff{t}} | AiryAi(z)=((z)^(5/ 4)* exp(-(2/ 3)* (z)^(3/ 2)))/((2)^(7/ 2)* Pi)* int(((t)^(- 1/ 2)* exp(-(2/ 3)* (t)^(3/ 2))*AiryAi(t))/((z)^(3/ 2)+ (t)^(3/ 2)), t = 0..infinity) |
AiryAi[z]=Divide[(z)^(5/ 4)* Exp[-(2/ 3)* (z)^(3/ 2)],(2)^(7/ 2)* Pi]* Integrate[Divide[(t)^(- 1/ 2)* Exp[-(2/ 3)* (t)^(3/ 2)]*AiryAi[t],(z)^(3/ 2)+ (t)^(3/ 2)], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 9.10.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\!\!\int_{0}^{v}\AiryAi@{t}\diff{t}\diff{v} = x\int_{0}^{x}\AiryAi@{t}\diff{t}-\AiryAi'@{x}+\AiryAi'@{0}} | int(int(AiryAi(t), t = 0..v), v = 0..x)= x*int(AiryAi(t), t = 0..x)- subs( temp=x, diff( AiryAi(temp), temp$(1) ) )+ subs( temp=0, diff( AiryAi(temp), temp$(1) ) ) |
Integrate[Integrate[AiryAi[t], {t, 0, v}], {v, 0, x}]= x*Integrate[AiryAi[t], {t, 0, x}]- (D[AiryAi[temp], {temp, 1}]/.temp-> x)+ (D[AiryAi[temp], {temp, 1}]/.temp-> 0) |
Failure | Failure | Skip | Successful |
| 9.10.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\!\!\int_{0}^{v}\AiryBi@{t}\diff{t}\diff{v} = x\int_{0}^{x}\AiryBi@{t}\diff{t}-\AiryBi'@{x}+\AiryBi'@{0}} | int(int(AiryBi(t), t = 0..v), v = 0..x)= x*int(AiryBi(t), t = 0..x)- subs( temp=x, diff( AiryBi(temp), temp$(1) ) )+ subs( temp=0, diff( AiryBi(temp), temp$(1) ) ) |
Integrate[Integrate[AiryBi[t], {t, 0, v}], {v, 0, x}]= x*Integrate[AiryBi[t], {t, 0, x}]- (D[AiryBi[temp], {temp, 1}]/.temp-> x)+ (D[AiryBi[temp], {temp, 1}]/.temp-> 0) |
Failure | Failure | Skip | Successful |
| 9.11.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[3]{w}{z}-4z\deriv{w}{z}-2w = 0} | diff(w, [z$(3)])- 4*z*diff(w, z)- 2*w = 0 |
D[w, {z, 3}]- 4*z*D[w, z]- 2*w = 0 |
Failure | Failure | Skip | Error |
| 9.11.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\AiryAi^{2}@{z},\AiryAi@{z}\AiryBi@{z},\AiryBi^{2}@{z}} = 2\pi^{-3}} | ((AiryAi(z))^(2))*diff(AiryAi(z)*AiryBi(z)*(AiryBi(z))^(2), z)-diff((AiryAi(z))^(2), z)*(AiryAi(z)*AiryBi(z)*(AiryBi(z))^(2))= 2*(Pi)^(- 3) |
Wronskian[{(AiryAi[z])^(2), AiryAi[z]*AiryBi[z]*(AiryBi[z])^(2)}, z]= 2*(Pi)^(- 3) |
Failure | Failure | Fail -.6004096260e-1-.6097999473e-2*I <- {z = 2^(1/2)+I*2^(1/2)}-.6004096260e-1+.6097999473e-2*I <- {z = 2^(1/2)-I*2^(1/2)}-21.32909363+6.905982746*I <- {z = -2^(1/2)-I*2^(1/2)}-21.32909363-6.905982746*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-0.060040962617560416, -0.006097999474625239] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.060040962617560416, 0.006097999474625239] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-21.329093714189053, 6.905982810760452] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-21.329093714189053, -6.905982810760452] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.11.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi^{2}@{x} = \frac{1}{4\pi\sqrt{3}}\int_{0}^{\infty}\BesselJ{0}@{\tfrac{1}{12}t^{3}+xt}t\diff{t}} | (AiryAi(x))^(2)=(1)/(4*Pi*sqrt(3))*int(BesselJ(0, (1)/(12)*(t)^(3)+ x*t)*t, t = 0..infinity) |
(AiryAi[x])^(2)=Divide[1,4*Pi*Sqrt[3]]*Integrate[BesselJ[0, Divide[1,12]*(t)^(3)+ x*t]*t, {t, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 9.11.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi^{2}@{z}+\AiryBi^{2}@{z} = \frac{1}{\pi^{3/2}}\int_{0}^{\infty}\exp@{zt-\tfrac{1}{12}t^{3}}t^{-1/2}\diff{t}} | (AiryAi(z))^(2)+ (AiryBi(z))^(2)=(1)/((Pi)^(3/ 2))*int(exp(z*t -(1)/(12)*(t)^(3))*(t)^(- 1/ 2), t = 0..infinity) |
(AiryAi[z])^(2)+ (AiryBi[z])^(2)=Divide[1,(Pi)^(3/ 2)]*Integrate[Exp[z*t -Divide[1,12]*(t)^(3)]*(t)^(- 1/ 2), {t, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 9.11.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\frac{\diff{z}}{\AiryAi^{2}@{z}} = \pi\frac{\AiryBi@{z}}{\AiryAi@{z}}} | int((1)/((AiryAi(z))^(2)), z)= Pi*(AiryBi(z))/(AiryAi(z)) |
Integrate[Divide[1,(AiryAi[z])^(2)], z]= Pi*Divide[AiryBi[z],AiryAi[z]] |
Failure | Successful | Skip | - |
| 9.11.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\frac{\diff{z}}{\AiryAi@{z}\AiryBi@{z}} = \pi\ln@{\frac{\AiryBi@{z}}{\AiryAi@{z}}}} | int((1)/(AiryAi(z)*AiryBi(z)), z)= Pi*ln((AiryBi(z))/(AiryAi(z))) |
Integrate[Divide[1,AiryAi[z]*AiryBi[z]], z]= Pi*Log[Divide[AiryBi[z],AiryAi[z]]] |
Failure | Failure | Skip | Successful |
| 9.11.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\frac{\AiryAi@{z}\AiryBi@{z}}{\left(\AiryAi^{2}@{z}+\AiryBi^{2}@{z}\right)^{2}}\diff{z} = \frac{\pi}{2}\frac{\AiryBi^{2}@{z}}{\AiryAi^{2}@{z}+\AiryBi^{2}@{z}}} | int((AiryAi(z)*AiryBi(z))/(((AiryAi(z))^(2)+ (AiryBi(z))^(2))^(2)), z)=(Pi)/(2)*((AiryBi(z))^(2))/((AiryAi(z))^(2)+ (AiryBi(z))^(2)) |
Integrate[Divide[AiryAi[z]*AiryBi[z],((AiryAi[z])^(2)+ (AiryBi[z])^(2))^(2)], z]=Divide[Pi,2]*Divide[(AiryBi[z])^(2),(AiryAi[z])^(2)+ (AiryBi[z])^(2)] |
Failure | Failure | Skip | Successful |
| 9.11.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\alpha-1}\AiryAi^{2}@{t}\diff{t} = \frac{2\EulerGamma@{\alpha}}{\pi^{1/2}12^{(2\alpha+5)/6}\EulerGamma@{\frac{1}{3}\alpha+\frac{5}{6}}}} | int((t)^(alpha - 1)* (AiryAi(t))^(2), t = 0..infinity)=(2*GAMMA(alpha))/((Pi)^(1/ 2)* (12)^((2*alpha + 5)/ 6)* GAMMA((1)/(3)*alpha +(5)/(6))) |
Integrate[(t)^(\[Alpha]- 1)* (AiryAi[t])^(2), {t, 0, Infinity}]=Divide[2*Gamma[\[Alpha]],(Pi)^(1/ 2)* (12)^((2*\[Alpha]+ 5)/ 6)* Gamma[Divide[1,3]*\[Alpha]+Divide[5,6]]] |
Failure | Failure | Skip | Successful |
| 9.11.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}\AiryAi^{3}@{t}\diff{t} = \frac{\EulerGamma^{2}@{\frac{1}{3}}}{4\pi^{2}}} | int((AiryAi(t))^(3), t = - infinity..infinity)=((GAMMA((1)/(3)))^(2))/(4*(Pi)^(2)) |
Integrate[(AiryAi[t])^(3), {t, - Infinity, Infinity}]=Divide[(Gamma[Divide[1,3]])^(2),4*(Pi)^(2)] |
Failure | Failure | Skip | Error |
| 9.11.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}\AiryAi^{2}@{t}\AiryBi@{t}\diff{t} = \frac{\EulerGamma^{2}@{\frac{1}{3}}}{4\sqrt{3}\pi^{2}}} | int((AiryAi(t))^(2)* AiryBi(t), t = - infinity..infinity)=((GAMMA((1)/(3)))^(2))/(4*sqrt(3)*(Pi)^(2)) |
Integrate[(AiryAi[t])^(2)* AiryBi[t], {t, - Infinity, Infinity}]=Divide[(Gamma[Divide[1,3]])^(2),4*Sqrt[3]*(Pi)^(2)] |
Failure | Failure | Skip | Error |
| 9.11.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\AiryAi^{4}@{t}\diff{t} = \frac{\ln@@{3}}{24\pi^{2}}} | int((AiryAi(t))^(4), t = 0..infinity)=(ln(3))/(24*(Pi)^(2)) |
Integrate[(AiryAi[t])^(4), {t, 0, Infinity}]=Divide[Log[3],24*(Pi)^(2)] |
Failure | Failure | Skip | Fail
Complex[1.4095755333126005, 1.4142135623730951] <- {Rule[Integrate[Power[AiryAi[t], 4], {t, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4095755333126005, -1.4142135623730951] <- {Rule[Integrate[Power[AiryAi[t], 4], {t, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4188515914335897, -1.4142135623730951] <- {Rule[Integrate[Power[AiryAi[t], 4], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4188515914335897, 1.4142135623730951] <- {Rule[Integrate[Power[AiryAi[t], 4], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.11.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{\diff{t}}{\AiryAi^{2}@{t}+\AiryBi^{2}@{t}} = \int_{0}^{\infty}\frac{t\diff{t}}{\AiryAi'^{2}@{t}+\AiryBi'^{2}@{t}}} | int((1)/((AiryAi(t))^(2)+ (AiryBi(t))^(2)), t = 0..infinity)= int((t)/((subs( temp=t, diff( AiryAi(temp), temp$(1) ) ))^(2)+ (subs( temp=t, diff( AiryBi(temp), temp$(1) ) ))^(2)), t = 0..infinity) |
Integrate[Divide[1,(AiryAi[t])^(2)+ (AiryBi[t])^(2)], {t, 0, Infinity}]= Integrate[Divide[t,((D[AiryAi[temp], {temp, 1}]/.temp-> t))^(2)+ ((D[AiryBi[temp], {temp, 1}]/.temp-> t))^(2)], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 9.11.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{t\diff{t}}{\AiryAi'^{2}@{t}+\AiryBi'^{2}@{t}} = \frac{\pi^{2}}{6}} | int((t)/((subs( temp=t, diff( AiryAi(temp), temp$(1) ) ))^(2)+ (subs( temp=t, diff( AiryBi(temp), temp$(1) ) ))^(2)), t = 0..infinity)=((Pi)^(2))/(6) |
Integrate[Divide[t,((D[AiryAi[temp], {temp, 1}]/.temp-> t))^(2)+ ((D[AiryBi[temp], {temp, 1}]/.temp-> t))^(2)], {t, 0, Infinity}]=Divide[(Pi)^(2),6] |
Failure | Failure | Skip | Fail
Complex[-0.23072050447513104, 1.4142135623730951] <- {Rule[Integrate[Times[t, Power[Plus[Power[AiryAiPrime[t], 2], Power[AiryBiPrime[t], 2]], -1]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.23072050447513104, -1.4142135623730951] <- {Rule[Integrate[Times[t, Power[Plus[Power[AiryAiPrime[t], 2], Power[AiryBiPrime[t], 2]], -1]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.0591476292213216, -1.4142135623730951] <- {Rule[Integrate[Times[t, Power[Plus[Power[AiryAiPrime[t], 2], Power[AiryBiPrime[t], 2]], -1]], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.0591476292213216, 1.4142135623730951] <- {Rule[Integrate[Times[t, Power[Plus[Power[AiryAiPrime[t], 2], Power[AiryBiPrime[t], 2]], -1]], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 9.12.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}-zw = \frac{1}{\pi}} | diff(w, [z$(2)])- z*w =(1)/(Pi) |
D[w, {z, 2}]- z*w =Divide[1,Pi] |
Failure | Failure | Fail -.3183098861-3.999999998*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-4.318309884-0.*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-.3183098861+3.999999998*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}3.681690112-0.*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Error |
| 9.12.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerGi@{z} = \AiryBi@{z}\int_{z}^{\infty}\AiryAi@{t}\diff{t}+\AiryAi@{z}\int_{0}^{z}\AiryBi@{t}\diff{t}} | AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))= AiryBi(z)*int(AiryAi(t), t = z..infinity)+ AiryAi(z)*int(AiryBi(t), t = 0..z) |
ScorerGi[z]= AiryBi[z]*Integrate[AiryAi[t], {t, z, Infinity}]+ AiryAi[z]*Integrate[AiryBi[t], {t, 0, z}] |
Successful | Failure | - | Successful |
| 9.12.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerHi@{z} = \AiryBi@{z}\int_{-\infty}^{z}\AiryAi@{t}\diff{t}-\AiryAi@{z}\int_{-\infty}^{z}\AiryBi@{t}\diff{t}} | AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))= AiryBi(z)*int(AiryAi(t), t = - infinity..z)- AiryAi(z)*int(AiryBi(t), t = - infinity..z) |
ScorerHi[z]= AiryBi[z]*Integrate[AiryAi[t], {t, - Infinity, z}]- AiryAi[z]*Integrate[AiryBi[t], {t, - Infinity, z}] |
Successful | Failure | - | Skip |
| 9.12.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerGi@{0} = \tfrac{1}{2}\ScorerHi@{0}} | AiryBi(0)*(int(AiryAi(t), t = (0) .. infinity))+AiryAi(0)*(int(AiryBi(t), t = 0 .. (0)))=(1)/(2)*AiryBi(0)*(int(AiryAi(t), t = -infinity .. (0)))-AiryAi(0)*(int(AiryBi(t), t = -infinity .. (0))) |
ScorerGi[0]=Divide[1,2]*ScorerHi[0] |
Successful | Successful | - | - |
| 9.12.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\ScorerHi@{0} = \tfrac{1}{3}\AiryBi@{0}} | (1)/(2)*AiryBi(0)*(int(AiryAi(t), t = -infinity .. (0)))-AiryAi(0)*(int(AiryBi(t), t = -infinity .. (0)))=(1)/(3)*AiryBi(0) |
Divide[1,2]*ScorerHi[0]=Divide[1,3]*AiryBi[0] |
Successful | Successful | - | - |
| 9.12.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerGi'@{0} = \tfrac{1}{2}\ScorerHi'@{0}} | subs( temp=0, diff( AiryBi(temp)*(int(AiryAi(t), t = (temp) .. infinity))+AiryAi(temp)*(int(AiryBi(t), t = 0 .. (temp))), temp$(1) ) )=(1)/(2)*subs( temp=0, diff( AiryBi(temp)*(int(AiryAi(t), t = -infinity .. (temp)))-AiryAi(temp)*(int(AiryBi(t), t = -infinity .. (temp))), temp$(1) ) ) |
(D[ScorerGi[temp], {temp, 1}]/.temp-> 0)=Divide[1,2]*(D[ScorerHi[temp], {temp, 1}]/.temp-> 0) |
Successful | Successful | - | - |
| 9.12.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\ScorerHi'@{0} = \tfrac{1}{3}\AiryBi'@{0}} | (1)/(2)*subs( temp=0, diff( AiryBi(temp)*(int(AiryAi(t), t = -infinity .. (temp)))-AiryAi(temp)*(int(AiryBi(t), t = -infinity .. (temp))), temp$(1) ) )=(1)/(3)*subs( temp=0, diff( AiryBi(temp), temp$(1) ) ) |
Divide[1,2]*(D[ScorerHi[temp], {temp, 1}]/.temp-> 0)=Divide[1,3]*(D[AiryBi[temp], {temp, 1}]/.temp-> 0) |
Successful | Successful | - | - |
| 9.12.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{3}\AiryBi'@{0} = 1\Big{/}\left(3^{5/6}\EulerGamma@{\tfrac{1}{3}}\right)} | (1)/(3)*subs( temp=0, diff( AiryBi(temp), temp$(1) ) )= 1/((3)^(5/ 6)* GAMMA((1)/(3))) |
Divide[1,3]*(D[AiryBi[temp], {temp, 1}]/.temp-> 0)= 1/((3)^(5/ 6)* Gamma[Divide[1,3]]) |
Successful | Successful | - | - |
| 9.12.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerGi@{z}+\ScorerHi@{z} = \AiryBi@{z}} | AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))+ AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))= AiryBi(z) |
ScorerGi[z]+ ScorerHi[z]= AiryBi[z] |
Successful | Successful | - | - |
| 9.12.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerGi@{z} = \tfrac{1}{2}e^{\pi i/3}\ScorerHi@{ze^{-2\pi i/3}}+\tfrac{1}{2}e^{-\pi i/3}\ScorerHi@{ze^{2\pi i/3}}} | AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))=(1)/(2)*exp(Pi*I/ 3)*AiryBi(z*exp(- 2*Pi*I/ 3))*(int(AiryAi(t), t = -infinity .. (z*exp(- 2*Pi*I/ 3))))-AiryAi(z*exp(- 2*Pi*I/ 3))*(int(AiryBi(t), t = -infinity .. (z*exp(- 2*Pi*I/ 3))))+(1)/(2)*exp(- Pi*I/ 3)*AiryBi(z*exp(2*Pi*I/ 3))*(int(AiryAi(t), t = -infinity .. (z*exp(2*Pi*I/ 3))))-AiryAi(z*exp(2*Pi*I/ 3))*(int(AiryBi(t), t = -infinity .. (z*exp(2*Pi*I/ 3)))) |
ScorerGi[z]=Divide[1,2]*Exp[Pi*I/ 3]*ScorerHi[z*Exp[- 2*Pi*I/ 3]]+Divide[1,2]*Exp[- Pi*I/ 3]*ScorerHi[z*Exp[2*Pi*I/ 3]] |
Failure | Successful | Fail .6194989342-.2058648052*I <- {z = 2^(1/2)+I*2^(1/2)}.6194989342+.2058648052*I <- {z = 2^(1/2)-I*2^(1/2)}1.652883055+1.203317832*I <- {z = -2^(1/2)-I*2^(1/2)}1.652883056-1.203317832*I <- {z = -2^(1/2)+I*2^(1/2)} |
- |
| 9.12.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerGi@{z} = e^{-\pi i/3}\ScorerHi@{ze^{+ 2\pi i/3}}+ i\AiryAi@{z}} | AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))= exp(- Pi*I/ 3)*AiryBi(z*exp(+ 2*Pi*I/ 3))*(int(AiryAi(t), t = -infinity .. (z*exp(+ 2*Pi*I/ 3))))-AiryAi(z*exp(+ 2*Pi*I/ 3))*(int(AiryBi(t), t = -infinity .. (z*exp(+ 2*Pi*I/ 3))))+ I*AiryAi(z) |
ScorerGi[z]= Exp[- Pi*I/ 3]*ScorerHi[z*Exp[+ 2*Pi*I/ 3]]+ I*AiryAi[z] |
Failure | Successful | Fail .1301354555-.9994650010e-1*I <- {z = 2^(1/2)+I*2^(1/2)}.5221313133+.4008588212*I <- {z = 2^(1/2)-I*2^(1/2)}.340645583e-1+.100353266*I <- {z = -2^(1/2)-I*2^(1/2)}2.243678175-.228349494*I <- {z = -2^(1/2)+I*2^(1/2)} |
- |
| 9.12.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerGi@{z} = e^{+\pi i/3}\ScorerHi@{ze^{- 2\pi i/3}}- i\AiryAi@{z}} | AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))= exp(+ Pi*I/ 3)*AiryBi(z*exp(- 2*Pi*I/ 3))*(int(AiryAi(t), t = -infinity .. (z*exp(- 2*Pi*I/ 3))))-AiryAi(z*exp(- 2*Pi*I/ 3))*(int(AiryBi(t), t = -infinity .. (z*exp(- 2*Pi*I/ 3))))- I*AiryAi(z) |
ScorerGi[z]= Exp[+ Pi*I/ 3]*ScorerHi[z*Exp[- 2*Pi*I/ 3]]- I*AiryAi[z] |
Failure | Successful | Fail .5221313133-.4008588212*I <- {z = 2^(1/2)+I*2^(1/2)}.1301354555+.9994650010e-1*I <- {z = 2^(1/2)-I*2^(1/2)}2.243678175+.228349494*I <- {z = -2^(1/2)-I*2^(1/2)}.340645583e-1-.100353266*I <- {z = -2^(1/2)+I*2^(1/2)} |
- |
| 9.12.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerHi@{z} = e^{+ 2\pi i/3}\ScorerHi@{ze^{+ 2\pi i/3}}+2e^{-\pi i/6}\AiryAi@{ze^{- 2\pi i/3}}} | AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))= exp(+ 2*Pi*I/ 3)*AiryBi(z*exp(+ 2*Pi*I/ 3))*(int(AiryAi(t), t = -infinity .. (z*exp(+ 2*Pi*I/ 3))))-AiryAi(z*exp(+ 2*Pi*I/ 3))*(int(AiryBi(t), t = -infinity .. (z*exp(+ 2*Pi*I/ 3))))+ 2*exp(- Pi*I/ 6)*AiryAi(z*exp(- 2*Pi*I/ 3)) |
ScorerHi[z]= Exp[+ 2*Pi*I/ 3]*ScorerHi[z*Exp[+ 2*Pi*I/ 3]]+ 2*Exp[- Pi*I/ 6]*AiryAi[z*Exp[- 2*Pi*I/ 3]] |
Failure | Successful | Fail -.1731124148-.2254012203*I <- {z = 2^(1/2)+I*2^(1/2)}.6943078446-.9043579630*I <- {z = 2^(1/2)-I*2^(1/2)}.1738169473-.59001540e-1*I <- {z = -2^(1/2)-I*2^(1/2)}-.3955129264-3.886164592*I <- {z = -2^(1/2)+I*2^(1/2)} |
- |
| 9.12.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerHi@{z} = e^{- 2\pi i/3}\ScorerHi@{ze^{- 2\pi i/3}}+2e^{+\pi i/6}\AiryAi@{ze^{+ 2\pi i/3}}} | AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))= exp(- 2*Pi*I/ 3)*AiryBi(z*exp(- 2*Pi*I/ 3))*(int(AiryAi(t), t = -infinity .. (z*exp(- 2*Pi*I/ 3))))-AiryAi(z*exp(- 2*Pi*I/ 3))*(int(AiryBi(t), t = -infinity .. (z*exp(- 2*Pi*I/ 3))))+ 2*exp(+ Pi*I/ 6)*AiryAi(z*exp(+ 2*Pi*I/ 3)) |
ScorerHi[z]= Exp[- 2*Pi*I/ 3]*ScorerHi[z*Exp[- 2*Pi*I/ 3]]+ 2*Exp[+ Pi*I/ 6]*AiryAi[z*Exp[+ 2*Pi*I/ 3]] |
Failure | Successful | Fail .6943078446+.9043579630*I <- {z = 2^(1/2)+I*2^(1/2)}-.1731124148+.2254012203*I <- {z = 2^(1/2)-I*2^(1/2)}-.3955129264+3.886164592*I <- {z = -2^(1/2)-I*2^(1/2)}.1738169473+.59001540e-1*I <- {z = -2^(1/2)+I*2^(1/2)} |
- |
| 9.12.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerGi@{z} = \frac{3^{-2/3}}{\pi}\*\sum_{k=0}^{\infty}\cos@{\frac{2k-1}{3}\pi}\EulerGamma@{\frac{k+1}{3}}\frac{(3^{1/3}z)^{k}}{k!}} | AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))=((3)^(- 2/ 3))/(Pi)* sum(cos((2*k - 1)/(3)*Pi)*GAMMA((k + 1)/(3))*(((3)^(1/ 3)* z)^(k))/(factorial(k)), k = 0..infinity) |
ScorerGi[z]=Divide[(3)^(- 2/ 3),Pi]* Sum[Cos[Divide[2*k - 1,3]*Pi]*Gamma[Divide[k + 1,3]]*Divide[((3)^(1/ 3)* z)^(k),(k)!], {k, 0, Infinity}] |
Failure | Successful | Skip | - |
| 9.12.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerGi'@{z} = \frac{3^{-1/3}}{\pi}\*\sum_{k=0}^{\infty}\cos@{\frac{2k+1}{3}\pi}\EulerGamma@{\frac{k+2}{3}}\frac{(3^{1/3}z)^{k}}{k!}} | subs( temp=z, diff( AiryBi(temp)*(int(AiryAi(t), t = (temp) .. infinity))+AiryAi(temp)*(int(AiryBi(t), t = 0 .. (temp))), temp$(1) ) )=((3)^(- 1/ 3))/(Pi)* sum(cos((2*k + 1)/(3)*Pi)*GAMMA((k + 2)/(3))*(((3)^(1/ 3)* z)^(k))/(factorial(k)), k = 0..infinity) |
(D[ScorerGi[temp], {temp, 1}]/.temp-> z)=Divide[(3)^(- 1/ 3),Pi]* Sum[Cos[Divide[2*k + 1,3]*Pi]*Gamma[Divide[k + 2,3]]*Divide[((3)^(1/ 3)* z)^(k),(k)!], {k, 0, Infinity}] |
Failure | Successful | Skip | - |
| 9.12.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerHi@{z} = \frac{3^{-2/3}}{\pi}\sum_{k=0}^{\infty}\EulerGamma@{\frac{k+1}{3}}\frac{(3^{1/3}z)^{k}}{k!}} | AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))=((3)^(- 2/ 3))/(Pi)*sum(GAMMA((k + 1)/(3))*(((3)^(1/ 3)* z)^(k))/(factorial(k)), k = 0..infinity) |
ScorerHi[z]=Divide[(3)^(- 2/ 3),Pi]*Sum[Gamma[Divide[k + 1,3]]*Divide[((3)^(1/ 3)* z)^(k),(k)!], {k, 0, Infinity}] |
Failure | Successful | Skip | - |
| 9.12.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerHi'@{z} = \frac{3^{-1/3}}{\pi}\sum_{k=0}^{\infty}\EulerGamma@{\frac{k+2}{3}}\frac{(3^{1/3}z)^{k}}{k!}} | subs( temp=z, diff( AiryBi(temp)*(int(AiryAi(t), t = -infinity .. (temp)))-AiryAi(temp)*(int(AiryBi(t), t = -infinity .. (temp))), temp$(1) ) )=((3)^(- 1/ 3))/(Pi)*sum(GAMMA((k + 2)/(3))*(((3)^(1/ 3)* z)^(k))/(factorial(k)), k = 0..infinity) |
(D[ScorerHi[temp], {temp, 1}]/.temp-> z)=Divide[(3)^(- 1/ 3),Pi]*Sum[Gamma[Divide[k + 2,3]]*Divide[((3)^(1/ 3)* z)^(k),(k)!], {k, 0, Infinity}] |
Failure | Successful | Skip | - |
| 9.12.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerGi@{x} = \frac{1}{\pi}\int_{0}^{\infty}\sin@{\tfrac{1}{3}t^{3}+xt}\diff{t}} | AiryBi(x)*(int(AiryAi(t), t = (x) .. infinity))+AiryAi(x)*(int(AiryBi(t), t = 0 .. (x)))=(1)/(Pi)*int(sin((1)/(3)*(t)^(3)+ x*t), t = 0..infinity) |
ScorerGi[x]=Divide[1,Pi]*Integrate[Sin[Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 9.12.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerHi@{z} = \frac{1}{\pi}\int_{0}^{\infty}\exp@{-\tfrac{1}{3}t^{3}+zt}\diff{t}} | AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))=(1)/(Pi)*int(exp(-(1)/(3)*(t)^(3)+ z*t), t = 0..infinity) |
ScorerHi[z]=Divide[1,Pi]*Integrate[Exp[-Divide[1,3]*(t)^(3)+ z*t], {t, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 9.12.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerGi@{z} = -\frac{1}{\pi}\int_{0}^{\infty}\exp@{-\tfrac{1}{3}t^{3}-\tfrac{1}{2}zt}\cos@{\tfrac{1}{2}\sqrt{3}zt+\tfrac{2}{3}\pi}\diff{t}} | AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))= -(1)/(Pi)*int(exp(-(1)/(3)*(t)^(3)-(1)/(2)*z*t)*cos((1)/(2)*sqrt(3)*z*t +(2)/(3)*Pi), t = 0..infinity) |
ScorerGi[z]= -Divide[1,Pi]*Integrate[Exp[-Divide[1,3]*(t)^(3)-Divide[1,2]*z*t]*Cos[Divide[1,2]*Sqrt[3]*z*t +Divide[2,3]*Pi], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 9.12.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerHi@{-z} = \frac{4z^{2}}{3^{3/2}\pi^{2}}\int_{0}^{\infty}\frac{\modBesselK{1/3}@{t}}{\zeta^{2}+t^{2}}\diff{t}} | AiryBi(- z)*(int(AiryAi(t), t = -infinity .. (- z)))-AiryAi(- z)*(int(AiryBi(t), t = -infinity .. (- z)))=(4*(z)^(2))/((3)^(3/ 2)* (Pi)^(2))*int((BesselK(1/ 3, t))/((2)/(3)*((z)^((3)/(2)))^(2)+ (t)^(2)), t = 0..infinity) |
ScorerHi[- z]=Divide[4*(z)^(2),(3)^(3/ 2)* (Pi)^(2)]*Integrate[Divide[BesselK[1/ 3, t],Divide[2,3]*((z)^(Divide[3,2]))^(2)+ (t)^(2)], {t, 0, Infinity}] |
Failure | Failure | Skip | Fail
Complex[0.04337928599820519, -0.02597020526100885] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.04337928599820519, 0.02597020526100885] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} |
| 9.12.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ScorerHi@{z} = \frac{3^{-2/3}}{2\pi^{2}i}\int_{-i\infty}^{i\infty}\EulerGamma@{\tfrac{1}{3}+\tfrac{1}{3}t}\EulerGamma@{-t}(3^{1/3}e^{\pi i}z)^{t}\diff{t}} | AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))=((3)^(- 2/ 3))/(2*(Pi)^(2)* I)*int(GAMMA((1)/(3)+(1)/(3)*t)*GAMMA(- t)*((3)^(1/ 3)* exp(Pi*I)*z)^(t), t = - I*infinity..I*infinity) |
ScorerHi[z]=Divide[(3)^(- 2/ 3),2*(Pi)^(2)* I]*Integrate[Gamma[Divide[1,3]+Divide[1,3]*t]*Gamma[- t]*((3)^(1/ 3)* Exp[Pi*I]*z)^(t), {t, - I*Infinity, I*Infinity}] |
Failure | Failure | Skip | Error |
| 9.13.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{t} = \tfrac{1}{4}m^{2}t^{m-2}w} | diff(w, [t$(2)])=(1)/(4)*(m)^(2)* (t)^(m - 2)* w |
D[w, {t, 2}]=Divide[1,4]*(m)^(2)* (t)^(m - 2)* w |
Failure | Failure | Fail -.2500000000 <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 1}-1.414213562-1.414213562*I <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 2}-0.-8.999999996*I <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 3}-0.+.2500000000*I <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), m = 1}... skip entries to safe data |
Error |
| 9.13.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{1}(x,\alpha) = \frac{1}{(\alpha+2)^{1/(\alpha+2)}}\*\EulerGamma@{\frac{\alpha+1}{\alpha+2}}x^{1/2}\BesselJ{-1/(\alpha+2)}@{\frac{2}{\alpha+2}x^{(\alpha+2)/2}}} | U[1]*(x , alpha)=(1)/((alpha + 2)^(1/(alpha + 2)))* GAMMA((alpha + 1)/(alpha + 2))*(x)^(1/ 2)* BesselJ(- 1/(alpha + 2), (2)/(alpha + 2)*(x)^((alpha + 2)/ 2)) |
Subscript[U, 1]*(x , \[Alpha])=Divide[1,(\[Alpha]+ 2)^(1/(\[Alpha]+ 2))]* Gamma[Divide[\[Alpha]+ 1,\[Alpha]+ 2]]*(x)^(1/ 2)* BesselJ[- 1/(\[Alpha]+ 2), Divide[2,\[Alpha]+ 2]*(x)^((\[Alpha]+ 2)/ 2)] |
Failure | Failure | Error | Error |
| 9.13.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{2}(x,\alpha) = (\alpha+2)^{1/(\alpha+2)}\*\EulerGamma@{\frac{\alpha+3}{\alpha+2}}x^{1/2}\BesselJ{1/(\alpha+2)}@{\frac{2}{\alpha+2}x^{(\alpha+2)/2}}} | U[2]*(x , alpha)=(alpha + 2)^(1/(alpha + 2))* GAMMA((alpha + 3)/(alpha + 2))*(x)^(1/ 2)* BesselJ(1/(alpha + 2), (2)/(alpha + 2)*(x)^((alpha + 2)/ 2)) |
Subscript[U, 2]*(x , \[Alpha])=(\[Alpha]+ 2)^(1/(\[Alpha]+ 2))* Gamma[Divide[\[Alpha]+ 3,\[Alpha]+ 2]]*(x)^(1/ 2)* BesselJ[1/(\[Alpha]+ 2), Divide[2,\[Alpha]+ 2]*(x)^((\[Alpha]+ 2)/ 2)] |
Failure | Failure | Error | Error |
| 9.13.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{1}(x,\alpha) = \frac{\pi^{1/2}}{2^{(m+2)/(2m)}\EulerGamma@{1/m}}\left(W_{m}(t)+W_{m}(-t)\right)} | U[1]*(x , alpha)=((Pi)^(1/ 2))/((2)^((m + 2)/(2*m))* GAMMA(1/ m))*(W[m]*(t)+ W[m]*(- t)) |
Subscript[U, 1]*(x , \[Alpha])=Divide[(Pi)^(1/ 2),(2)^((m + 2)/(2*m))* Gamma[1/ m]]*(Subscript[W, m]*(t)+ Subscript[W, m]*(- t)) |
Failure | Failure | Error | Error |
| 9.13.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{2}(x,\alpha) = \frac{\pi^{1/2}m^{2/m}}{2^{(m+2)/(2m)}\EulerGamma@{-1/m}}\left(W_{m}(t){-}W_{m}(-t)\right)} | U[2]*(x , alpha)=((Pi)^(1/ 2)* (m)^(2/ m))/((2)^((m + 2)/(2*m))* GAMMA(- 1/ m))*(W[m]*(t)- W[m]*(- t)) |
Subscript[U, 2]*(x , \[Alpha])=Divide[(Pi)^(1/ 2)* (m)^(2/ m),(2)^((m + 2)/(2*m))* Gamma[- 1/ m]]*(Subscript[W, m]*(t)- Subscript[W, m]*(- t)) |
Failure | Failure | Skip | Error |