Parabolic Cylinder Functions - 12.14 The Function

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
12.14.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraW@{a}{0} = 2^{-\frac{3}{4}}\left|\frac{\EulerGamma@{\tfrac{1}{4}+\tfrac{1}{2}ia}}{\EulerGamma@{\tfrac{3}{4}+\tfrac{1}{2}ia}}\right|^{\frac{1}{2}}}
\paraW@{a}{0} = 2^{-\frac{3}{4}}\left|\frac{\EulerGamma@{\tfrac{1}{4}+\tfrac{1}{2}ia}}{\EulerGamma@{\tfrac{3}{4}+\tfrac{1}{2}ia}}\right|^{\frac{1}{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(\tfrac{1}{4}+\tfrac{1}{2}\iunit a)} > 0, \realpart@@{(\tfrac{3}{4}+\tfrac{1}{2}\iunit a)} > 0} 
Error

Sqrt[(Sqrt[1+Exp[2*Pi*(a)]]-Exp[Pi*(a)])/2] * Exp[Divide[Pi*(a),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 - I*(a), 0 * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 + I*(a), 0 * Exp[Divide[Pi*I,4]]] ) == (2)^(-Divide[3,4])*(Abs[Divide[Gamma[Divide[1,4]+Divide[1,2]*I*a],Gamma[Divide[3,4]+Divide[1,2]*I*a]]])^(Divide[1,2])
Missing Macro Error Failure -
Failed [6 / 6]
Result: Plus[-0.6502446611528931, Times[0.2167171091323973, Plus[Times[Complex[2.1101734540747557, 0.09157129889910319], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[Complex[0.5, -1.5]]]]]]]], Times[Complex[2.1101734540747557, -0.09157129889910319], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[Complex[0.5, -1.5]]]]]]]]]]]
Test Values: {Rule[a, -1.5]}


Result: Plus[-0.6502446611528931, Times[0.15393043293932354, Plus[Times[Complex[2.1101734540747557, -0.09157129889910319], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[Complex[0.5, 1.5]]]]]]]], Times[Complex[2.1101734540747557, 0.09157129889910319], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[Complex[0.5, 1.5]]]]]]]]]]]
Test Values: {Rule[a, 1.5]}

... skip entries to safe data
12.14.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraW'@{a}{0} = -2^{-\frac{1}{4}}\left|\frac{\EulerGamma@{\tfrac{3}{4}+\tfrac{1}{2}ia}}{\EulerGamma@{\tfrac{1}{4}+\tfrac{1}{2}ia}}\right|^{\frac{1}{2}}}
\paraW'@{a}{0} = -2^{-\frac{1}{4}}\left|\frac{\EulerGamma@{\tfrac{3}{4}+\tfrac{1}{2}ia}}{\EulerGamma@{\tfrac{1}{4}+\tfrac{1}{2}ia}}\right|^{\frac{1}{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(\tfrac{3}{4}+\tfrac{1}{2}\iunit a)} > 0, \realpart@@{(\tfrac{1}{4}+\tfrac{1}{2}\iunit a)} > 0} 
Error

(D[Sqrt[(Sqrt[1+Exp[2*Pi*(a)]]-Exp[Pi*(a)])/2] * Exp[Divide[Pi*(a),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 - I*(a), temp * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 + I*(a), temp * Exp[Divide[Pi*I,4]]] ), {temp, 1}]/.temp-> 0) == - (2)^(-Divide[1,4])*(Abs[Divide[Gamma[Divide[3,4]+Divide[1,2]*I*a],Gamma[Divide[1,4]+Divide[1,2]*I*a]]])^(Divide[1,2])
Missing Macro Error Failure -
Failed [6 / 6]
Result: Plus[0.7689413383471582, Times[0.2167171091323973, Plus[Times[Complex[-1.704391150531108, -1.8258251253417301], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[Complex[0.5, -1.5]]]]]]]]], Times[Complex[-1.704391150531108, 1.8258251253417301], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[Complex[0.5, -1.5]]]]]]]]]]]]
Test Values: {Rule[a, -1.5]}


Result: Plus[0.7689413383471582, Times[0.15393043293932354, Plus[Times[Complex[-1.704391150531108, 1.8258251253417301], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[Complex[0.5, 1.5]]]]]]]]], Times[Complex[-1.704391150531108, -1.8258251253417301], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[Complex[0.5, 1.5]]]]]]]]]]]]
Test Values: {Rule[a, 1.5]}

... skip entries to safe data
12.14.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\paraW@{a}{x},\paraW@{a}{-x}} = 1}
\Wronskian@{\paraW@{a}{x},\paraW@{a}{-x}} = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
Error

Wronskian[{Sqrt[(Sqrt[1+Exp[2*Pi*(a)]]-Exp[Pi*(a)])/2] * Exp[Divide[Pi*(a),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 - I*(a), x * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 + I*(a), x * Exp[Divide[Pi*I,4]]] ), Sqrt[(Sqrt[1+Exp[2*Pi*(a)]]-Exp[Pi*(a)])/2] * Exp[Divide[Pi*(a),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 - I*(a), - x * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 + I*(a), - x * Exp[Divide[Pi*I,4]]] )}, x] == 1
Missing Macro Error Aborted -
Failed [18 / 18]
Result: Plus[-1.0, Times[0.49552852896181854, Power[2.718281828459045, Plus[-2.356194490192345, Times[Complex[0.0, -1.0], Arg[GAMMA[Complex[0.5, -1.5]]]]]], Plus[Complex[6.858735565841029, 8.017762045530217], Times[Complex[-3.325234230733274, 7.771974729433958], Power[2.718281828459045, Times[Complex[0.0, 1.0], Arg[GAMMA[Complex[0.5, -1.5]]]]]], Times[Complex[-0.5683445061301408, 1.832896863544324], Power[2.718281828459045, Times[Complex[0.0, 1.0], Arg[GAMMA[Complex[0.5, -1.5]]]]], Plus[Complex[-3.829019967249232, -1.729594934825754], Times[Complex[-1.3099191255337557, -0.33304402326481836], Power[2.718281828459045, Times[Complex[0.0, 1.0], Arg[GAMMA[Complex[0.5, -1.5]]]]]]]], Times[Complex[-0.6925599504260578, -1.7781797223294367], Power[2.718281828459045, Times[Complex[0.0, 1.0], Arg[GAMMA[Complex[0.5, -1.5]]]]], Plus[Complex[1.1964059764236668, -0.5640566230504777], Times[Complex[1.7883988364886165, 3.791736125757196], Power[2.718281828459045, Times<syntaxhighlight lang=mathematica>Result: Plus[-1.0, Times[0.49552852896181854, Power[2.718281828459045, Plus[-2.356194490192345, Times[Complex[0.0, -1.0], Arg[GAMMA[Complex[0.5, -1.5]]]]]], Plus[Complex[6.858735565841018, 8.01776204553021], Times[Complex[2.1162015796075306, -3.4943658291294586], Power[2.718281828459045, Times[Complex[0.0, 1.0], Arg[GAMMA[Complex[0.5, -1.5]]]]]], Times[Complex[1.7644828790311722, 1.0958018333501354], Power[2.718281828459045, Times[Complex[0.0, 1.0], Arg[GAMMA[Complex[0.5, -1.5]]]]], Plus[Complex[-1.886026428459961, 2.3891008291554687], Times[Complex[0.20069396529457476, -1.987274101858182], Power[2.718281828459045, Times[Complex[0.0, 1.0], Arg[GAMMA[Complex[0.5, -1.5]]]]]]]], Times[Complex[1.683947543704261, -1.245446997525291], Power[2.718281828459045, Times[Complex[0.0, 1.0], Arg[GAMMA[Complex[0.5, -1.5]]]]], Plus[Complex[1.1608218100872771, 1.6575881988304835], Times[Complex[3.0041801875943053, -0.5876813330718609], Power[2.718281828459045, Times[Complex[0.0, 1.0], Arg[GAMMA[Complex[0.5, -1.5]]]]]]]]]]]
Test Values: {Rule[a, -1.5], Rule[x, 0.5]}

... skip entries to safe data
12.14.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraW@{a}{x} = \sqrt{k/2}\,e^{\frac{1}{4}\pi a}\left(e^{i\rho}\paraU@{ia}{xe^{-\pi i/4}}+e^{-i\rho}\paraU@{-ia}{xe^{\pi i/4}}\right)}
\paraW@{a}{x} = \sqrt{k/2}\,e^{\frac{1}{4}\pi a}\left(e^{i\rho}\paraU@{ia}{xe^{-\pi i/4}}+e^{-i\rho}\paraU@{-ia}{xe^{\pi i/4}}\right)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(\tfrac{1}{2}+\iunit a)} > 0} 
Error

Sqrt[(Sqrt[1+Exp[2*Pi*(a)]]-Exp[Pi*(a)])/2] * Exp[Divide[Pi*(a),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 - I*(a), x * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 + I*(a), x * Exp[Divide[Pi*I,4]]] ) == Sqrt[(Sqrt[1 + Exp[2*Pi*a]]- Exp[Pi*a])/2]*Exp[Divide[1,4]*Pi*a]*(Exp[I*(Divide[1,8]*Pi +Divide[1,2]*(Arg[Gamma[Divide[1,2]+ I*a]]))]*ParabolicCylinderD[- 1/2 -(I*a), x*Exp[- Pi*I/4]]+ Exp[- I*(Divide[1,8]*Pi +Divide[1,2]*(Arg[Gamma[Divide[1,2]+ I*a]]))]*ParabolicCylinderD[- 1/2 -(- I*a), x*Exp[Pi*I/4]])
Missing Macro Error Failure -
Failed [18 / 18]
Result: Plus[Complex[0.7504500073451766, 0.0], Times[0.2167171091323973, Plus[Times[Complex[-0.5683445061301404, -1.832896863544323], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[Complex[0.5, -1.5]]]]]]]], Times[Complex[-0.5683445061301404, 1.832896863544323], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[Complex[0.5, -1.5]]]]]]]]]]]
Test Values: {Rule[a, -1.5], Rule[x, 1.5]}


Result: Plus[Complex[-0.17071363418721158, 0.0], Times[0.2167171091323973, Plus[Times[Complex[1.764482879031172, -1.0958018333501351], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[Complex[0.5, -1.5]]]]]]]], Times[Complex[1.764482879031172, 1.0958018333501351], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[Complex[0.5, -1.5]]]]]]]]]]]
Test Values: {Rule[a, -1.5], Rule[x, 0.5]}

... skip entries to safe data
12.14.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraW@{a}{x} = \paraW@{a}{0}w_{1}(a,x)+\paraW'@{a}{0}w_{2}(a,x)}
\paraW@{a}{x} = \paraW@{a}{0}w_{1}(a,x)+\paraW'@{a}{0}w_{2}(a,x)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
Error

Sqrt[(Sqrt[1+Exp[2*Pi*(a)]]-Exp[Pi*(a)])/2] * Exp[Divide[Pi*(a),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 - I*(a), x * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 + I*(a), x * Exp[Divide[Pi*I,4]]] ) == Sqrt[(Sqrt[1+Exp[2*Pi*(a)]]-Exp[Pi*(a)])/2] * Exp[Divide[Pi*(a),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 - I*(a), 0 * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 + I*(a), 0 * Exp[Divide[Pi*I,4]]] )*(Sum[Subscript[\[Alpha], n][a]*Divide[(x)^(2*n),(2*n)!], {n, 0, Infinity}, GenerateConditions->None])+ (D[Sqrt[(Sqrt[1+Exp[2*Pi*(a)]]-Exp[Pi*(a)])/2] * Exp[Divide[Pi*(a),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 - I*(a), temp * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 + I*(a), temp * Exp[Divide[Pi*I,4]]] ), {temp, 1}]/.temp-> 0)*(Sum[Subscript[\[Beta], n][a]*Divide[(x)^(2*n + 1),(2*n + 1)!], {n, 0, Infinity}, GenerateConditions->None])
Missing Macro Error Aborted - Skipped - Because timed out
12.14#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{0}(a) = 1}
\alpha_{0}(a) = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
alpha[0](a) = 1
 
Subscript[\[Alpha], 0][a] == 1
 Skipped - no semantic math Skipped - no semantic math - -
12.14#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{1}(a) = a}
\alpha_{1}(a) = a		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
alpha[1](a) = a
 
Subscript[\[Alpha], 1][a] == a
 Skipped - no semantic math Skipped - no semantic math - -
12.14#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{0}(a) = 1}
\beta_{0}(a) = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
beta[0](a) = 1
 
Subscript[\[Beta], 0][a] == 1
 Skipped - no semantic math Skipped - no semantic math - -
12.14#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{1}(a) = a}
\beta_{1}(a) = a		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
beta[1](a) = a
 
Subscript[\[Beta], 1][a] == a
 Skipped - no semantic math Skipped - no semantic math - -
12.14.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraW@{0}{+ x} = 2^{-\frac{5}{4}}\sqrt{\pi x}\left(\BesselJ{-\frac{1}{4}}@{\tfrac{1}{4}x^{2}}-\BesselJ{\frac{1}{4}}@{\tfrac{1}{4}x^{2}}\right)}
\paraW@{0}{+ x} = 2^{-\frac{5}{4}}\sqrt{\pi x}\left(\BesselJ{-\frac{1}{4}}@{\tfrac{1}{4}x^{2}}-\BesselJ{\frac{1}{4}}@{\tfrac{1}{4}x^{2}}\right)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{((-\frac{1}{4})+k+1)} > 0, \realpart@@{((\frac{1}{4})+k+1)} > 0} 
Error

Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), + x * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), + x * Exp[Divide[Pi*I,4]]] ) == (2)^(-Divide[5,4])*Sqrt[Pi*x]*(BesselJ[-Divide[1,4], Divide[1,4]*(x)^(2)]- BesselJ[Divide[1,4], Divide[1,4]*(x)^(2)])
Missing Macro Error Failure -
Failed [3 / 3]
Result: Plus[-0.22960009916312846, Times[0.4550898605622274, Plus[Times[Complex[0.5125789656744846, -0.578293218532047], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[0.5125789656744846, 0.578293218532047], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]
Test Values: {Rule[x, 1.5]}


Result: Plus[-0.7771899742615831, Times[0.4550898605622274, Plus[Times[Complex[1.0093127652068992, -0.20538419268274744], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[1.0093127652068992, 0.20538419268274744], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]
Test Values: {Rule[x, 0.5]}

... skip entries to safe data
12.14.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraW@{0}{- x} = 2^{-\frac{5}{4}}\sqrt{\pi x}\left(\BesselJ{-\frac{1}{4}}@{\tfrac{1}{4}x^{2}}+\BesselJ{\frac{1}{4}}@{\tfrac{1}{4}x^{2}}\right)}
\paraW@{0}{- x} = 2^{-\frac{5}{4}}\sqrt{\pi x}\left(\BesselJ{-\frac{1}{4}}@{\tfrac{1}{4}x^{2}}+\BesselJ{\frac{1}{4}}@{\tfrac{1}{4}x^{2}}\right)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{((-\frac{1}{4})+k+1)} > 0, \realpart@@{((\frac{1}{4})+k+1)} > 0} 
Error

Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), - x * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), - x * Exp[Divide[Pi*I,4]]] ) == (2)^(-Divide[5,4])*Sqrt[Pi*x]*(BesselJ[-Divide[1,4], Divide[1,4]*(x)^(2)]+ BesselJ[Divide[1,4], Divide[1,4]*(x)^(2)])
Missing Macro Error Failure -
Failed [3 / 3]
Result: Plus[-1.6050209192353964, Times[0.4550898605622274, Plus[Times[Complex[1.669165402738578, 0.5782932185320475], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[1.669165402738578, -0.5782932185320475], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]
Test Values: {Rule[x, 1.5]}


Result: Plus[-1.2656786607564097, Times[0.4550898605622274, Plus[Times[Complex[1.4200811505723943, 0.2053841926827476], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[1.4200811505723943, -0.2053841926827476], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]
Test Values: {Rule[x, 0.5]}

... skip entries to safe data
12.14.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{x}\paraW@{0}{+ x} = -2^{-\frac{9}{4}}x\sqrt{\pi x}\left(\BesselJ{\frac{3}{4}}@{\tfrac{1}{4}x^{2}}+\BesselJ{-\frac{3}{4}}@{\tfrac{1}{4}x^{2}}\right)}
\deriv{}{x}\paraW@{0}{+ x} = -2^{-\frac{9}{4}}x\sqrt{\pi x}\left(\BesselJ{\frac{3}{4}}@{\tfrac{1}{4}x^{2}}+\BesselJ{-\frac{3}{4}}@{\tfrac{1}{4}x^{2}}\right)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{((\frac{3}{4})+k+1)} > 0, \realpart@@{((-\frac{3}{4})+k+1)} > 0} 
Error

D[Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), + x * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), + x * Exp[Divide[Pi*I,4]]] ), x] == - (2)^(-Divide[9,4])* x*Sqrt[Pi*x]*(BesselJ[Divide[3,4], Divide[1,4]*(x)^(2)]+ BesselJ[-Divide[3,4], Divide[1,4]*(x)^(2)])
Missing Macro Error Aborted -
Failed [3 / 3]
Result: Plus[0.6138624292597322, Times[0.4550898605622274, Plus[Times[Complex[-0.6342811205261311, 0.23110891742402956], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.6342811205261311, -0.23110891742402956], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]
Test Values: {Rule[x, 1.5]}


Result: Plus[0.497609493984496, Times[0.4550898605622274, Plus[Times[Complex[-0.5880519854532475, 0.008953751453165265], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.5880519854532475, -0.008953751453165265], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]
Test Values: {Rule[x, 0.5]}

... skip entries to safe data
12.14.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{x}\paraW@{0}{- x} = -2^{-\frac{9}{4}}x\sqrt{\pi x}\left(\BesselJ{\frac{3}{4}}@{\tfrac{1}{4}x^{2}}-\BesselJ{-\frac{3}{4}}@{\tfrac{1}{4}x^{2}}\right)}
\deriv{}{x}\paraW@{0}{- x} = -2^{-\frac{9}{4}}x\sqrt{\pi x}\left(\BesselJ{\frac{3}{4}}@{\tfrac{1}{4}x^{2}}-\BesselJ{-\frac{3}{4}}@{\tfrac{1}{4}x^{2}}\right)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{((\frac{3}{4})+k+1)} > 0, \realpart@@{((-\frac{3}{4})+k+1)} > 0} 
Error

D[Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), - x * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), - x * Exp[Divide[Pi*I,4]]] ), x] == - (2)^(-Divide[9,4])* x*Sqrt[Pi*x]*(BesselJ[Divide[3,4], Divide[1,4]*(x)^(2)]- BesselJ[-Divide[3,4], Divide[1,4]*(x)^(2)])
Missing Macro Error Aborted -
Failed [3 / 3]
Result: Plus[-0.06418969137726768, Times[0.4550898605622274, Plus[Times[Complex[0.17206328567807166, 0.23110891742402973], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[0.17206328567807166, -0.23110891742402973], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]
Test Values: {Rule[x, 1.5]}


Result: Plus[-0.4763137641163559, Times[0.4550898605622274, Plus[Times[Complex[0.5701444825469169, 0.008953751453165182], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[0.5701444825469169, -0.008953751453165182], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]
Test Values: {Rule[x, 0.5]}

... skip entries to safe data
12.14.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(a,x) = e^{-\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{1}{4}-\tfrac{1}{2}ia}{\tfrac{1}{2}}{\tfrac{1}{2}ix^{2}}}
w_{1}(a,x) = e^{-\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{1}{4}-\tfrac{1}{2}ia}{\tfrac{1}{2}}{\tfrac{1}{2}ix^{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(sum(alpha[n](a)*((x)^(2*n))/(factorial(2*n)), n = 0..infinity)) = exp(-(1)/(4)*I*(x)^(2))*KummerM((1)/(4)-(1)/(2)*I*a, (1)/(2), (1)/(2)*I*(x)^(2))

(Sum[Subscript[\[Alpha], n][a]*Divide[(x)^(2*n),(2*n)!], {n, 0, Infinity}, GenerateConditions->None]) == Exp[-Divide[1,4]*I*(x)^(2)]*Hypergeometric1F1[Divide[1,4]-Divide[1,2]*I*a, Divide[1,2], Divide[1,2]*I*(x)^(2)]
Failure Failure Skipped - Because timed out Skipped - Because timed out
12.14.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{1}{4}-\tfrac{1}{2}ia}{\tfrac{1}{2}}{\tfrac{1}{2}ix^{2}} = e^{\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{1}{4}+\tfrac{1}{2}ia}{\tfrac{1}{2}}{-\tfrac{1}{2}ix^{2}}}
e^{-\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{1}{4}-\tfrac{1}{2}ia}{\tfrac{1}{2}}{\tfrac{1}{2}ix^{2}} = e^{\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{1}{4}+\tfrac{1}{2}ia}{\tfrac{1}{2}}{-\tfrac{1}{2}ix^{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
exp(-(1)/(4)*I*(x)^(2))*KummerM((1)/(4)-(1)/(2)*I*a, (1)/(2), (1)/(2)*I*(x)^(2)) = exp((1)/(4)*I*(x)^(2))*KummerM((1)/(4)+(1)/(2)*I*a, (1)/(2), -(1)/(2)*I*(x)^(2))

Exp[-Divide[1,4]*I*(x)^(2)]*Hypergeometric1F1[Divide[1,4]-Divide[1,2]*I*a, Divide[1,2], Divide[1,2]*I*(x)^(2)] == Exp[Divide[1,4]*I*(x)^(2)]*Hypergeometric1F1[Divide[1,4]+Divide[1,2]*I*a, Divide[1,2], -Divide[1,2]*I*(x)^(2)]
Failure Successful Successful [Tested: 18] Successful [Tested: 18]
12.14.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{2}(a,x) = xe^{-\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{3}{4}-\tfrac{1}{2}ia}{\tfrac{3}{2}}{\tfrac{1}{2}ix^{2}}}
w_{2}(a,x) = xe^{-\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{3}{4}-\tfrac{1}{2}ia}{\tfrac{3}{2}}{\tfrac{1}{2}ix^{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(sum(beta[n](a)*((x)^(2*n + 1))/(factorial(2*n + 1)), n = 0..infinity)) = x*exp(-(1)/(4)*I*(x)^(2))*KummerM((3)/(4)-(1)/(2)*I*a, (3)/(2), (1)/(2)*I*(x)^(2))

(Sum[Subscript[\[Beta], n][a]*Divide[(x)^(2*n + 1),(2*n + 1)!], {n, 0, Infinity}, GenerateConditions->None]) == x*Exp[-Divide[1,4]*I*(x)^(2)]*Hypergeometric1F1[Divide[3,4]-Divide[1,2]*I*a, Divide[3,2], Divide[1,2]*I*(x)^(2)]
Failure Failure Skipped - Because timed out Skipped - Because timed out
12.14.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle xe^{-\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{3}{4}-\tfrac{1}{2}ia}{\tfrac{3}{2}}{\tfrac{1}{2}ix^{2}} = xe^{\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{3}{4}+\tfrac{1}{2}ia}{\tfrac{3}{2}}{-\tfrac{1}{2}ix^{2}}}
xe^{-\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{3}{4}-\tfrac{1}{2}ia}{\tfrac{3}{2}}{\tfrac{1}{2}ix^{2}} = xe^{\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{3}{4}+\tfrac{1}{2}ia}{\tfrac{3}{2}}{-\tfrac{1}{2}ix^{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
x*exp(-(1)/(4)*I*(x)^(2))*KummerM((3)/(4)-(1)/(2)*I*a, (3)/(2), (1)/(2)*I*(x)^(2)) = x*exp((1)/(4)*I*(x)^(2))*KummerM((3)/(4)+(1)/(2)*I*a, (3)/(2), -(1)/(2)*I*(x)^(2))

x*Exp[-Divide[1,4]*I*(x)^(2)]*Hypergeometric1F1[Divide[3,4]-Divide[1,2]*I*a, Divide[3,2], Divide[1,2]*I*(x)^(2)] == x*Exp[Divide[1,4]*I*(x)^(2)]*Hypergeometric1F1[Divide[3,4]+Divide[1,2]*I*a, Divide[3,2], -Divide[1,2]*I*(x)^(2)]
Failure Successful Successful [Tested: 18] Successful [Tested: 18]
12.14.E17 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraW@{a}{x} = \sqrt{\frac{2k}{x}}\left(s_{1}(a,x)\cos@@{\omega}-s_{2}(a,x)\sin@@{\omega}\right)}
\paraW@{a}{x} = \sqrt{\frac{2k}{x}}\left(s_{1}(a,x)\cos@@{\omega}-s_{2}(a,x)\sin@@{\omega}\right)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(\tfrac{1}{2}+\iunit a)} > 0} 
Error

Sqrt[(Sqrt[1+Exp[2*Pi*(a)]]-Exp[Pi*(a)])/2] * Exp[Divide[Pi*(a),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 - I*(a), x * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 + I*(a), x * Exp[Divide[Pi*I,4]]] ) == Sqrt[Divide[2*(Sqrt[1 + Exp[2*Pi*a]]- Exp[Pi*a]),x]]*(Subscript[s, 1][a , x]* Cos[Divide[1,4]*(x)^(2)- a*Log[x]+Divide[1,4]*Pi +Divide[1,2]*(Arg[Gamma[Divide[1,2]+ I*a]])]- Subscript[s, 2][a , x]* Sin[Divide[1,4]*(x)^(2)- a*Log[x]+Divide[1,4]*Pi +Divide[1,2]*(Arg[Gamma[Divide[1,2]+ I*a]])])
Missing Macro Error Failure - Error
12.14.E18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraW@{a}{-x} = \sqrt{\frac{2}{kx}}\left(s_{1}(a,x)\sin@@{\omega}+s_{2}(a,x)\cos@@{\omega}\right)}
\paraW@{a}{-x} = \sqrt{\frac{2}{kx}}\left(s_{1}(a,x)\sin@@{\omega}+s_{2}(a,x)\cos@@{\omega}\right)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(\tfrac{1}{2}+\iunit a)} > 0} 
Error

Sqrt[(Sqrt[1+Exp[2*Pi*(a)]]-Exp[Pi*(a)])/2] * Exp[Divide[Pi*(a),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 - I*(a), - x * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(a)]]/2)] * ParabolicCylinderD[- 1/2 + I*(a), - x * Exp[Divide[Pi*I,4]]] ) == Sqrt[Divide[2,k*x]]*(Subscript[s, 1][a , x]* Sin[Divide[1,4]*(x)^(2)- a*Log[x]+Divide[1,4]*Pi +Divide[1,2]*(Arg[Gamma[Divide[1,2]+ I*a]])]+ Subscript[s, 2][a , x]* Cos[Divide[1,4]*(x)^(2)- a*Log[x]+Divide[1,4]*Pi +Divide[1,2]*(Arg[Gamma[Divide[1,2]+ I*a]])])
Missing Macro Error Failure - Error
12.14.E24 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{t} = \mu^{4}(1-t^{2})w}
\deriv[2]{w}{t} = \mu^{4}(1-t^{2})w		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
diff(w, [t$(2)]) = (mu)^(4)*(1 - (t)^(2))*w

D[w, {t, 2}] == \[Mu]^(4)*(1 - (t)^(2))*w
Failure Failure
Failed [300 / 300]
Result: -1.082531755+.6250000011*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, t = -3/2, w = 1/2*3^(1/2)+1/2*I}


Result: -.6250000011-1.082531755*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, t = -3/2, w = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[-1.0825317547305482, 0.6250000000000002]
Test Values: {Rule[t, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[-1.0825317547305482, 0.6250000000000002]
Test Values: {Rule[t, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
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