Difference between revisions of "Results of Airy and Related Functions"

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| [https://dlmf.nist.gov/9.2.E15 9.2.E15] || [[Item:Q2767|<math>\AiryBi@{-z} = e^{-\pi i/6}\AiryAi@{ze^{\pi i/3}}+e^{\pi i/6}\AiryAi@{ze^{-\pi i/3}}</math>]] || <code>AiryBi(- z)= exp(- Pi*I/ 6)*AiryAi(z*exp(Pi*I/ 3))+ exp(Pi*I/ 6)*AiryAi(z*exp(- Pi*I/ 3))</code> || <code>AiryBi[- z]= Exp[- Pi*I/ 6]*AiryAi[z*Exp[Pi*I/ 3]]+ Exp[Pi*I/ 6]*AiryAi[z*Exp[- Pi*I/ 3]]</code> || Failure || Successful || Successful || -  
 
| [https://dlmf.nist.gov/9.2.E15 9.2.E15] || [[Item:Q2767|<math>\AiryBi@{-z} = e^{-\pi i/6}\AiryAi@{ze^{\pi i/3}}+e^{\pi i/6}\AiryAi@{ze^{-\pi i/3}}</math>]] || <code>AiryBi(- z)= exp(- Pi*I/ 6)*AiryAi(z*exp(Pi*I/ 3))+ exp(Pi*I/ 6)*AiryAi(z*exp(- Pi*I/ 3))</code> || <code>AiryBi[- z]= Exp[- Pi*I/ 6]*AiryAi[z*Exp[Pi*I/ 3]]+ Exp[Pi*I/ 6]*AiryAi[z*Exp[- Pi*I/ 3]]</code> || Failure || Successful || Successful || -  
 
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| [https://dlmf.nist.gov/9.5.E1 9.5.E1] || [[Item:Q2773|<math>\AiryAi@{x} = \frac{1}{\pi}\int_{0}^{\infty}\cos@{\tfrac{1}{3}t^{3}+xt}\diff{t}</math>]] || <code>AiryAi(x)=(1)/(Pi)*int(cos((1)/(3)*(t)^(3)+ x*t), t = 0..infinity)</code> || <code>AiryAi[x]=Divide[1,Pi]*Integrate[Cos[Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}]</code> || Successful || Failure || - || Skip
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| [https://dlmf.nist.gov/9.5.E1 9.5.E1] || [[Item:Q2773|<math>\AiryAi@{x} = \frac{1}{\pi}\int_{0}^{\infty}\cos@{\tfrac{1}{3}t^{3}+xt}\diff{t}</math>]] || <code>AiryAi(x)=(1)/(Pi)*int(cos((1)/(3)*(t)^(3)+ x*t), t = 0..infinity)</code> || <code>AiryAi[x]=Divide[1,Pi]*Integrate[Cos[Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}]</code> || Successful || Failure || - || Successful
 
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| [https://dlmf.nist.gov/9.5.E2 9.5.E2] || [[Item:Q2774|<math>\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}</math>]] || <code>AiryAi(- x)=((x)^((1)/(2)))/(Pi)*int(cos((x)^((3)/(2))*((1)/(3)*(t)^(3)+ (t)^(2)-(2)/(3))), t = - 1..infinity)</code> || <code>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}]</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/9.5.E2 9.5.E2] || [[Item:Q2774|<math>\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}</math>]] || <code>AiryAi(- x)=((x)^((1)/(2)))/(Pi)*int(cos((x)^((3)/(2))*((1)/(3)*(t)^(3)+ (t)^(2)-(2)/(3))), t = - 1..infinity)</code> || <code>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}]</code> || Failure || Failure || Skip || Error  
 
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| [https://dlmf.nist.gov/9.5.E3 9.5.E3] || [[Item:Q2775|<math>\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}</math>]] || <code>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)</code> || <code>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}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[Plus[AiryBi[x], Times[Rational[-1, 6], Power[Pi, -1], Plus[Times[4, Pi, AiryBi[x]], Times[3, Power[x, 2], HypergeometricPFQ[{1}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[x, 3]]]]]], Times[-1, Power[Pi, -1], Plus[Times[Rational[1, 3], Pi, AiryBi[x]], Times[Rational[-1, 2], Power[x, 2], HypergeometricPFQ[{1}, {Rational[2, 3], Rational[5, 6], Rational[7, 6], Rational[4, 3]}, Times[Rational[1, 1296], Power[x, 6]]]], Times[Rational[-1, 40], Power[x, 5], HypergeometricPFQ[{1}, {Rational[7, 6], Rational[4, 3], Rational[5, 3], Rational[11, 6]}, Times[Rational[1, 1296], Power[x, 6]]]]]]], And[Element[x, Reals], Less[Re[x], 0]]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[Plus[AiryBi[x], Times[Rational[-1, 6], Power[Pi, -1], Plus[Times[4, Pi, AiryBi[x]], Times[3, Power[x, 2], HypergeometricPFQ[{1}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[x, 3]]]]]], Times[-1, Power[Pi, -1], Plus[Times[Rational[1, 3], Pi, AiryBi[x]], Times[Rational[-1, 2], Power[x, 2], HypergeometricPFQ[{1}, {Rational[2, 3], Rational[5, 6], Rational[7, 6], Rational[4, 3]}, Times[Rational[1, 1296], Power[x, 6]]]], Times[Rational[-1, 40], Power[x, 5], HypergeometricPFQ[{1}, {Rational[7, 6], Rational[4, 3], Rational[5, 3], Rational[11, 6]}, Times[Rational[1, 1296], Power[x, 6]]]]]]], And[Element[x, Reals], Less[Re[x], 0]]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[Plus[AiryBi[x], Times[Rational[-1, 6], Power[Pi, -1], Plus[Times[4, Pi, AiryBi[x]], Times[3, Power[x, 2], HypergeometricPFQ[{1}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[x, 3]]]]]], Times[-1, Power[Pi, -1], Plus[Times[Rational[1, 3], Pi, AiryBi[x]], Times[Rational[-1, 2], Power[x, 2], HypergeometricPFQ[{1}, {Rational[2, 3], Rational[5, 6], Rational[7, 6], Rational[4, 3]}, Times[Rational[1, 1296], Power[x, 6]]]], Times[Rational[-1, 40], Power[x, 5], HypergeometricPFQ[{1}, {Rational[7, 6], Rational[4, 3], Rational[5, 3], Rational[11, 6]}, Times[Rational[1, 1296], Power[x, 6]]]]]]], And[Element[x, Reals], Less[Re[x], 0]]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[Plus[AiryBi[x], Times[Rational[-1, 6], Power[Pi, -1], Plus[Times[4, Pi, AiryBi[x]], Times[3, Power[x, 2], HypergeometricPFQ[{1}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[x, 3]]]]]], Times[-1, Power[Pi, -1], Plus[Times[Rational[1, 3], Pi, AiryBi[x]], Times[Rational[-1, 2], Power[x, 2], HypergeometricPFQ[{1}, {Rational[2, 3], Rational[5, 6], Rational[7, 6], Rational[4, 3]}, Times[Rational[1, 1296], Power[x, 6]]]], Times[Rational[-1, 40], Power[x, 5], HypergeometricPFQ[{1}, {Rational[7, 6], Rational[4, 3], Rational[5, 3], Rational[11, 6]}, Times[Rational[1, 1296], Power[x, 6]]]]]]], And[Element[x, Reals], Less[Re[x], 0]]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
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| [https://dlmf.nist.gov/9.5.E3 9.5.E3] || [[Item:Q2775|<math>\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}</math>]] || <code>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)</code> || <code>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}]</code> || Failure || Failure || Skip || Successful
 
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| [https://dlmf.nist.gov/9.5.E4 9.5.E4] || [[Item:Q2776|<math>\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}</math>]] || <code>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))</code> || <code>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]}]</code> || Failure || Failure || Skip || Error
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| [https://dlmf.nist.gov/9.5.E4 9.5.E4] || [[Item:Q2776|<math>\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}</math>]] || <code>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))</code> || <code>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]}]</code> || Failure || Failure || Skip || Skip
 
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| [https://dlmf.nist.gov/9.5.E5 9.5.E5] || [[Item:Q2777|<math>\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}</math>]] || <code>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))</code> || <code>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]}]</code> || Failure || Failure || Skip || Error
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| [https://dlmf.nist.gov/9.5.E5 9.5.E5] || [[Item:Q2777|<math>\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}</math>]] || <code>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))</code> || <code>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]}]</code> || Failure || Failure || Skip || Skip
 
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| [https://dlmf.nist.gov/9.5.E6 9.5.E6] || [[Item:Q2778|<math>\AiryAi@{z} = \frac{\sqrt{3}}{2\pi}\int_{0}^{\infty}\exp@{-\frac{t^{3}}{3}-\frac{z^{3}}{3t^{3}}}\diff{t}</math>]] || <code>AiryAi(z)=(sqrt(3))/(2*Pi)*int(exp(-((t)^(3))/(3)-((z)^(3))/(3*(t)^(3))), t = 0..infinity)</code> || <code>AiryAi[z]=Divide[Sqrt[3],2*Pi]*Integrate[Exp[-Divide[(t)^(3),3]-Divide[(z)^(3),3*(t)^(3)]], {t, 0, Infinity}]</code> || Successful || Failure || - || Skip
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| [https://dlmf.nist.gov/9.5.E6 9.5.E6] || [[Item:Q2778|<math>\AiryAi@{z} = \frac{\sqrt{3}}{2\pi}\int_{0}^{\infty}\exp@{-\frac{t^{3}}{3}-\frac{z^{3}}{3t^{3}}}\diff{t}</math>]] || <code>AiryAi(z)=(sqrt(3))/(2*Pi)*int(exp(-((t)^(3))/(3)-((z)^(3))/(3*(t)^(3))), t = 0..infinity)</code> || <code>AiryAi[z]=Divide[Sqrt[3],2*Pi]*Integrate[Exp[-Divide[(t)^(3),3]-Divide[(z)^(3),3*(t)^(3)]], {t, 0, Infinity}]</code> || Successful || Failure || - || Successful
 
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| [https://dlmf.nist.gov/9.5.E7 9.5.E7] || [[Item:Q2779|<math>\AiryAi@{z} = \frac{e^{-\zeta}}{\pi}\int_{0}^{\infty}\exp@{-z^{\ifrac{1}{2}}t^{2}}\cos@{\tfrac{1}{3}t^{3}}\diff{t}</math>]] || <code>AiryAi(z)=(exp(-(2)/(3)*(z)^((3)/(2))))/(Pi)*int(exp(- (z)^((1)/(2))* (t)^(2))*cos((1)/(3)*(t)^(3)), t = 0..infinity)</code> || <code>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}]</code> || Failure || Failure || Skip || Successful
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| [https://dlmf.nist.gov/9.5.E7 9.5.E7] || [[Item:Q2779|<math>\AiryAi@{z} = \frac{e^{-\zeta}}{\pi}\int_{0}^{\infty}\exp@{-z^{\ifrac{1}{2}}t^{2}}\cos@{\tfrac{1}{3}t^{3}}\diff{t}</math>]] || <code>AiryAi(z)=(exp(-(2)/(3)*(z)^((3)/(2))))/(Pi)*int(exp(- (z)^((1)/(2))* (t)^(2))*cos((1)/(3)*(t)^(3)), t = 0..infinity)</code> || <code>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}]</code> || Failure || Failure || Skip || Skip
 
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| [https://dlmf.nist.gov/9.5.E8 9.5.E8] || [[Item:Q2780|<math>\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}</math>]] || <code>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)</code> || <code>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}]</code> || Failure || Failure || Skip || Error
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| [https://dlmf.nist.gov/9.5.E8 9.5.E8] || [[Item:Q2780|<math>\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}</math>]] || <code>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)</code> || <code>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}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.014252654553766713, -0.04024893384084034] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.014252654553766713, 0.04024893384084034] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
 
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| [https://dlmf.nist.gov/9.6.E2 9.6.E2] || [[Item:Q2782|<math>\AiryAi@{z} = \pi^{-1}\sqrt{z/3}\modBesselK{+ 1/3}@{\zeta}</math>]] || <code>AiryAi(z)= (Pi)^(- 1)*sqrt(z/ 3)*BesselK(+ 1/ 3, (2)/(3)*(z)^((3)/(2)))</code> || <code>AiryAi[z]= (Pi)^(- 1)*Sqrt[z/ 3]*BesselK[+ 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>2.833765278-.3039461853*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br><code>2.833765278+.3039461853*I <- {z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[2.8337652800788264, -0.3039461861802381] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.8337652800788264, 0.3039461861802381] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
 
| [https://dlmf.nist.gov/9.6.E2 9.6.E2] || [[Item:Q2782|<math>\AiryAi@{z} = \pi^{-1}\sqrt{z/3}\modBesselK{+ 1/3}@{\zeta}</math>]] || <code>AiryAi(z)= (Pi)^(- 1)*sqrt(z/ 3)*BesselK(+ 1/ 3, (2)/(3)*(z)^((3)/(2)))</code> || <code>AiryAi[z]= (Pi)^(- 1)*Sqrt[z/ 3]*BesselK[+ 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>2.833765278-.3039461853*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br><code>2.833765278+.3039461853*I <- {z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[2.8337652800788264, -0.3039461861802381] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.8337652800788264, 0.3039461861802381] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
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| [https://dlmf.nist.gov/9.6.E2 9.6.E2] || [[Item:Q2782|<math>\pi^{-1}\sqrt{z/3}\modBesselK{- 1/3}@{\zeta} = \tfrac{1}{3}\sqrt{z}\left(\modBesselI{-1/3}@{\zeta}-\modBesselI{1/3}@{\zeta}\right)</math>]] || <code>(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))))</code> || <code>(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])])</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/9.6.E2 9.6.E2] || [[Item:Q2782|<math>\pi^{-1}\sqrt{z/3}\modBesselK{- 1/3}@{\zeta} = \tfrac{1}{3}\sqrt{z}\left(\modBesselI{-1/3}@{\zeta}-\modBesselI{1/3}@{\zeta}\right)</math>]] || <code>(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))))</code> || <code>(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])])</code> || Successful || Successful || - || -  
 
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| [https://dlmf.nist.gov/9.6.E2 9.6.E2] || [[Item:Q2782|<math>\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}}</math>]] || <code>(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))</code> || <code>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]]</code> || Failure || Failure || Skip || Skip
+
| [https://dlmf.nist.gov/9.6.E2 9.6.E2] || [[Item:Q2782|<math>\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}}</math>]] || <code>(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))</code> || <code>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]]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-2.8337652800788247, 0.30394618618023783] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
 
|-
 
|-
| [https://dlmf.nist.gov/9.6.E2 9.6.E2] || [[Item:Q2782|<math>\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}}</math>]] || <code>(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))</code> || <code>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]]</code> || Successful || Failure || - || Skip
+
| [https://dlmf.nist.gov/9.6.E2 9.6.E2] || [[Item:Q2782|<math>\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}}</math>]] || <code>(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))</code> || <code>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]]</code> || Successful || Failure || - || Successful
 
|-
 
|-
| [https://dlmf.nist.gov/9.6.E2 9.6.E2] || [[Item:Q2782|<math>\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}}</math>]] || <code>(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))</code> || <code>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]]</code> || Failure || Failure || Skip || Skip
+
| [https://dlmf.nist.gov/9.6.E2 9.6.E2] || [[Item:Q2782|<math>\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}}</math>]] || <code>(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))</code> || <code>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]]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[2.8337652800788256, -0.3039461861802379] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.8337652800788247, -0.3039461861802372] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
 
|-
 
|-
| [https://dlmf.nist.gov/9.6.E2 9.6.E2] || [[Item:Q2782|<math>\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}}</math>]] || <code>(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))</code> || <code>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]]</code> || Successful || Failure || - || Skip
+
| [https://dlmf.nist.gov/9.6.E2 9.6.E2] || [[Item:Q2782|<math>\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}}</math>]] || <code>(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))</code> || <code>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]]</code> || Successful || Failure || - || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/9.6.E3 9.6.E3] || [[Item:Q2783|<math>\AiryAi'@{z} = -\pi^{-1}(z/\sqrt{3})\modBesselK{+ 2/3}@{\zeta}</math>]] || <code>subs( temp=z, diff( AiryAi(temp), temp$(1) ) )= - (Pi)^(- 1)*(z/sqrt(3))* BesselK(+ 2/ 3, (2)/(3)*(z)^((3)/(2)))</code> || <code>(D[AiryAi[temp], {temp, 1}]/.temp-> z)= - (Pi)^(- 1)*(z/Sqrt[3])* BesselK[+ 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.7883076520+3.485863958*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.7883076520-3.485863958*I <- {z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.7883076520663912, 3.485863960601928] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.7883076520663912, -3.485863960601928] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
 
| [https://dlmf.nist.gov/9.6.E3 9.6.E3] || [[Item:Q2783|<math>\AiryAi'@{z} = -\pi^{-1}(z/\sqrt{3})\modBesselK{+ 2/3}@{\zeta}</math>]] || <code>subs( temp=z, diff( AiryAi(temp), temp$(1) ) )= - (Pi)^(- 1)*(z/sqrt(3))* BesselK(+ 2/ 3, (2)/(3)*(z)^((3)/(2)))</code> || <code>(D[AiryAi[temp], {temp, 1}]/.temp-> z)= - (Pi)^(- 1)*(z/Sqrt[3])* BesselK[+ 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.7883076520+3.485863958*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.7883076520-3.485863958*I <- {z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.7883076520663912, 3.485863960601928] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.7883076520663912, -3.485863960601928] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
Line 77: Line 77:
 
| [https://dlmf.nist.gov/9.6.E3 9.6.E3] || [[Item:Q2783|<math>-\pi^{-1}(z/\sqrt{3})\modBesselK{- 2/3}@{\zeta} = (z/3)\left(\modBesselI{2/3}@{\zeta}-\modBesselI{-2/3}@{\zeta}\right)</math>]] || <code>- (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))))</code> || <code>- (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])])</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/9.6.E3 9.6.E3] || [[Item:Q2783|<math>-\pi^{-1}(z/\sqrt{3})\modBesselK{- 2/3}@{\zeta} = (z/3)\left(\modBesselI{2/3}@{\zeta}-\modBesselI{-2/3}@{\zeta}\right)</math>]] || <code>- (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))))</code> || <code>- (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])])</code> || Successful || Successful || - || -  
 
|-
 
|-
| [https://dlmf.nist.gov/9.6.E3 9.6.E3] || [[Item:Q2783|<math>(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}}</math>]] || <code>(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))</code> || <code>(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]]</code> || Failure || Failure || Skip || Skip
+
| [https://dlmf.nist.gov/9.6.E3 9.6.E3] || [[Item:Q2783|<math>(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}}</math>]] || <code>(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))</code> || <code>(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]]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.7883076520663918, -3.485863960601928] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
 
|-
 
|-
| [https://dlmf.nist.gov/9.6.E3 9.6.E3] || [[Item:Q2783|<math>\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}}</math>]] || <code>(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))</code> || <code>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]]</code> || Successful || Failure || - || Skip
+
| [https://dlmf.nist.gov/9.6.E3 9.6.E3] || [[Item:Q2783|<math>\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}}</math>]] || <code>(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))</code> || <code>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]]</code> || Successful || Failure || - || Successful
 
|-
 
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| [https://dlmf.nist.gov/9.6.E3 9.6.E3] || [[Item:Q2783|<math>\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}}</math>]] || <code>(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))</code> || <code>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]]</code> || Failure || Failure || Skip || Skip
+
| [https://dlmf.nist.gov/9.6.E3 9.6.E3] || [[Item:Q2783|<math>\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}}</math>]] || <code>(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))</code> || <code>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]]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.7883076520663909, 3.485863960601928] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7883076520663926, 3.485863960601928] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
 
|-
 
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| [https://dlmf.nist.gov/9.6.E3 9.6.E3] || [[Item:Q2783|<math>\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}}</math>]] || <code>(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))</code> || <code>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]]</code> || Successful || Failure || - || Skip
+
| [https://dlmf.nist.gov/9.6.E3 9.6.E3] || [[Item:Q2783|<math>\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}}</math>]] || <code>(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))</code> || <code>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]]</code> || Successful || Failure || - || Successful
 
|-
 
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| [https://dlmf.nist.gov/9.6.E4 9.6.E4] || [[Item:Q2784|<math>\AiryBi@{z} = \sqrt{z/3}\left(\modBesselI{1/3}@{\zeta}+\modBesselI{-1/3}@{\zeta}\right)</math>]] || <code>AiryBi(z)=sqrt(z/ 3)*(BesselI(1/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselI(- 1/ 3, (2)/(3)*(z)^((3)/(2))))</code> || <code>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])])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.323091265e-1+.116725832*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br><code>.323091265e-1-.116725832*I <- {z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.032309126109843156, 0.11672583064563491] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.032309126109843156, -0.11672583064563491] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
 
| [https://dlmf.nist.gov/9.6.E4 9.6.E4] || [[Item:Q2784|<math>\AiryBi@{z} = \sqrt{z/3}\left(\modBesselI{1/3}@{\zeta}+\modBesselI{-1/3}@{\zeta}\right)</math>]] || <code>AiryBi(z)=sqrt(z/ 3)*(BesselI(1/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselI(- 1/ 3, (2)/(3)*(z)^((3)/(2))))</code> || <code>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])])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.323091265e-1+.116725832*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br><code>.323091265e-1-.116725832*I <- {z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.032309126109843156, 0.11672583064563491] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.032309126109843156, -0.11672583064563491] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
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| [https://dlmf.nist.gov/9.6.E4 9.6.E4] || [[Item:Q2784|<math>\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)</math>]] || <code>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)))</code> || <code>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]])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.1681276560-1.475245556*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.1681276560+1.475245556*I <- {z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.16812765614504083, -1.4752455553622306] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.16812765614504083, 1.4752455553622306] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
 
| [https://dlmf.nist.gov/9.6.E4 9.6.E4] || [[Item:Q2784|<math>\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)</math>]] || <code>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)))</code> || <code>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]])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.1681276560-1.475245556*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.1681276560+1.475245556*I <- {z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.16812765614504083, -1.4752455553622306] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.16812765614504083, 1.4752455553622306] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
 
|-
 
|-
| [https://dlmf.nist.gov/9.6.E4 9.6.E4] || [[Item:Q2784|<math>\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)</math>]] || <code>(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)))</code> || <code>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]])</code> || Successful || Failure || - || Skip
+
| [https://dlmf.nist.gov/9.6.E4 9.6.E4] || [[Item:Q2784|<math>\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)</math>]] || <code>(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)))</code> || <code>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]])</code> || Successful || Failure || - || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/9.6.E5 9.6.E5] || [[Item:Q2785|<math>\AiryBi'@{z} = (z/\sqrt{3})\left(\modBesselI{2/3}@{\zeta}+\modBesselI{-2/3}@{\zeta}\right)</math>]] || <code>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))))</code> || <code>(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])])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.181539689+.267445042e-1*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br><code>.181539689-.267445042e-1*I <- {z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.18153969005752768, 0.026744504839266825] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.18153969005752768, -0.026744504839266825] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
 
| [https://dlmf.nist.gov/9.6.E5 9.6.E5] || [[Item:Q2785|<math>\AiryBi'@{z} = (z/\sqrt{3})\left(\modBesselI{2/3}@{\zeta}+\modBesselI{-2/3}@{\zeta}\right)</math>]] || <code>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))))</code> || <code>(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])])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.181539689+.267445042e-1*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br><code>.181539689-.267445042e-1*I <- {z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.18153969005752768, 0.026744504839266825] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.18153969005752768, -0.026744504839266825] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
Line 95: Line 95:
 
| [https://dlmf.nist.gov/9.6.E5 9.6.E5] || [[Item:Q2785|<math>(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)</math>]] || <code>(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)))</code> || <code>(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]])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.652162135+.3807815744*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br><code>1.652162135-.3807815744*I <- {z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.6521621352721998, 0.3807815736135619] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6521621352721998, -0.3807815736135619] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
 
| [https://dlmf.nist.gov/9.6.E5 9.6.E5] || [[Item:Q2785|<math>(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)</math>]] || <code>(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)))</code> || <code>(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]])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.652162135+.3807815744*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br><code>1.652162135-.3807815744*I <- {z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.6521621352721998, 0.3807815736135619] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6521621352721998, -0.3807815736135619] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
 
|-
 
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| [https://dlmf.nist.gov/9.6.E5 9.6.E5] || [[Item:Q2785|<math>\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)</math>]] || <code>(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)))</code> || <code>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]])</code> || Successful || Failure || - || Skip
+
| [https://dlmf.nist.gov/9.6.E5 9.6.E5] || [[Item:Q2785|<math>\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)</math>]] || <code>(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)))</code> || <code>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]])</code> || Successful || Failure || - || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/9.6.E6 9.6.E6] || [[Item:Q2786|<math>\AiryAi@{-z} = (\sqrt{z}/3)\left(\BesselJ{1/3}@{\zeta}+\BesselJ{-1/3}@{\zeta}\right)</math>]] || <code>AiryAi(- z)=(sqrt(z)/ 3)*(BesselJ(1/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselJ(- 1/ 3, (2)/(3)*(z)^((3)/(2))))</code> || <code>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])])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.5274645816-.7652257224e-1*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.5274645816+.7652257224e-1*I <- {z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.5274645818155765, -0.0765225723412053] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.5274645818155765, 0.0765225723412053] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
 
| [https://dlmf.nist.gov/9.6.E6 9.6.E6] || [[Item:Q2786|<math>\AiryAi@{-z} = (\sqrt{z}/3)\left(\BesselJ{1/3}@{\zeta}+\BesselJ{-1/3}@{\zeta}\right)</math>]] || <code>AiryAi(- z)=(sqrt(z)/ 3)*(BesselJ(1/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselJ(- 1/ 3, (2)/(3)*(z)^((3)/(2))))</code> || <code>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])])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.5274645816-.7652257224e-1*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.5274645816+.7652257224e-1*I <- {z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.5274645818155765, -0.0765225723412053] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.5274645818155765, 0.0765225723412053] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
Line 205: Line 205:
 
| [https://dlmf.nist.gov/9.8.E8 9.8.E8] || [[Item:Q2840|<math>\Airyphasederivphi@{x} = \atan@{\AiryAi'@{x}/\AiryBi'@{x}}</math>]] || <code>arctan(AiryAi(1, x)/AiryBi(1, x))= arctan(subs( temp=x, diff( AiryAi(temp), temp$(1) ) )/ subs( temp=x, diff( AiryBi(temp), temp$(1) ) ))</code> || <code>ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]= ArcTan[(D[AiryAi[temp], {temp, 1}]/.temp-> x)/ (D[AiryBi[temp], {temp, 1}]/.temp-> x)]</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/9.8.E8 9.8.E8] || [[Item:Q2840|<math>\Airyphasederivphi@{x} = \atan@{\AiryAi'@{x}/\AiryBi'@{x}}</math>]] || <code>arctan(AiryAi(1, x)/AiryBi(1, x))= arctan(subs( temp=x, diff( AiryAi(temp), temp$(1) ) )/ subs( temp=x, diff( AiryBi(temp), temp$(1) ) ))</code> || <code>ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]= ArcTan[(D[AiryAi[temp], {temp, 1}]/.temp-> x)/ (D[AiryBi[temp], {temp, 1}]/.temp-> x)]</code> || Successful || Successful || - || -  
 
|-
 
|-
| [https://dlmf.nist.gov/9.8.E9 9.8.E9] || [[Item:Q2841|<math>|x|^{1/2}\AirymodM^{2}@{x} = \tfrac{1}{2}\xi\left(\BesselJ{1/3}^{2}@{\xi}+\BesselY{1/3}^{2}@{\xi}\right)</math>]] || <code>(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))</code> || <code>(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))</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.159089025-.4715106810e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>15.06764807-.4715106810e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>340.9777186-.4715106810e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>1.159089025+.4715106810e-2*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>15.06764807+.4715106810e-2*I <- {xi = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>340.9777186+.4715106810e-2*I <- {xi = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>1.152932431-.2158756202e-1*I <- {xi = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>15.06149147-.2158756202e-1*I <- {xi = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>340.9715621-.2158756202e-1*I <- {xi = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>1.152932431+.2158756202e-1*I <- {xi = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>15.06149147+.2158756202e-1*I <- {xi = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>340.9715621+.2158756202e-1*I <- {xi = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.1590890245070966, -0.004715107328741586] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[15.06764807713232, -0.004715107328741586] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[340.9777188366776, -0.004715107328741586] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1590890245070966, 0.004715107328741586] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[15.06764807713232, 0.004715107328741586] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[340.9777188366776, 0.004715107328741586] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1529324301847828, -0.021587562167012547] <- {Rule[x, 1], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[15.061491482810007, -0.021587562167012547] <- {Rule[x, 2], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[340.9715622423553, -0.021587562167012547] <- {Rule[x, 3], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1529324301847828, 0.021587562167012547] <- {Rule[x, 1], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[15.061491482810007, 0.021587562167012547] <- {Rule[x, 2], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[340.9715622423553, 0.021587562167012547] <- {Rule[x, 3], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/9.8.E9 9.8.E9] || [[Item:Q2841|<math>|x|^{1/2}\AirymodM^{2}@{x} = \tfrac{1}{2}\xi\left(\BesselJ{1/3}^{2}@{\xi}+\BesselY{1/3}^{2}@{\xi}\right)</math>]] || <code>(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))</code> || <code>(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))</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.159089025-.4715106810e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>15.06764807-.4715106810e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>340.9777186-.4715106810e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>1.159089025+.4715106810e-2*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.1590890245070966, -0.004715107328741586] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[15.06764807713232, -0.004715107328741586] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[340.9777188366776, -0.004715107328741586] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1590890245070966, 0.004715107328741586] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
| [https://dlmf.nist.gov/9.8.E10 9.8.E10] || [[Item:Q2842|<math>|x|^{-1/2}\AirymodderivN^{2}@{x} = \tfrac{1}{2}\xi\left(\BesselJ{2/3}^{2}@{\xi}+\BesselY{2/3}^{2}@{\xi}\right)</math>]] || <code>(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))</code> || <code>(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))</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.5749530917+.6794393049e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>11.57260149+.6794393049e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>303.0362324+.6794393049e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>.5749530917-.6794393049e-2*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>11.57260149-.6794393049e-2*I <- {xi = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>303.0362324-.6794393049e-2*I <- {xi = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>.5801544350+.2618733010e-1*I <- {xi = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>11.57780284+.2618733010e-1*I <- {xi = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>303.0414338+.2618733010e-1*I <- {xi = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>.5801544350-.2618733010e-1*I <- {xi = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>11.57780284-.2618733010e-1*I <- {xi = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>303.0414338-.2618733010e-1*I <- {xi = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.5749530907924223, 0.0067943920267909685] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.572601490351364, 0.0067943920267909685] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[303.0362323510325, 0.0067943920267909685] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.5749530907924223, -0.0067943920267909685] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.572601490351364, -0.0067943920267909685] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[303.0362323510325, -0.0067943920267909685] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.5801544351344989, 0.026187329972932327] <- {Rule[x, 1], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.57780283469344, 0.026187329972932327] <- {Rule[x, 2], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[303.0414336953745, 0.026187329972932327] <- {Rule[x, 3], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.5801544351344989, -0.026187329972932327] <- {Rule[x, 1], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.57780283469344, -0.026187329972932327] <- {Rule[x, 2], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[303.0414336953745, -0.026187329972932327] <- {Rule[x, 3], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/9.8.E10 9.8.E10] || [[Item:Q2842|<math>|x|^{-1/2}\AirymodderivN^{2}@{x} = \tfrac{1}{2}\xi\left(\BesselJ{2/3}^{2}@{\xi}+\BesselY{2/3}^{2}@{\xi}\right)</math>]] || <code>(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))</code> || <code>(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))</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.5749530917+.6794393049e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>11.57260149+.6794393049e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>303.0362324+.6794393049e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>.5749530917-.6794393049e-2*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.5749530907924223, 0.0067943920267909685] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.572601490351364, 0.0067943920267909685] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[303.0362323510325, 0.0067943920267909685] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.5749530907924223, -0.0067943920267909685] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
| [https://dlmf.nist.gov/9.8.E11 9.8.E11] || [[Item:Q2843|<math>\Airyphasetheta@{x} = \tfrac{2}{3}\pi+\atan@{\BesselY{1/3}@{\xi}/\BesselJ{1/3}@{\xi}}</math>]] || <code>arctan(AiryAi(x)/AiryBi(x))=(2)/(3)*Pi + arctan(BesselY(1/ 3, xi)/ BesselJ(1/ 3, xi))</code> || <code>ArcTan[Divide[AiryAi[x], AiryBi[x]]]=Divide[2,3]*Pi + ArcTan[BesselY[1/ 3, \[Xi]]/ BesselJ[1/ 3, \[Xi]]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-2.062235934-1.435552558*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-2.163232204-1.435552558*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-2.173351447-1.435552558*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.062235934+1.435552558*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-2.163232204+1.435552558*I <- {xi = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-2.173351447+1.435552558*I <- {xi = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-2.452891048+1.446224854*I <- {xi = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-2.553887318+1.446224854*I <- {xi = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-2.564006561+1.446224854*I <- {xi = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-2.452891048-1.446224854*I <- {xi = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-2.553887318-1.446224854*I <- {xi = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-2.564006561-1.446224854*I <- {xi = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-2.062235934109286, -1.435552557338311] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.163232204380712, -1.435552557338311] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.17335144762396, -1.435552557338311] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.062235934109286, 1.435552557338311] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.163232204380712, 1.435552557338311] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.17335144762396, 1.435552557338311] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.4528910462808704, 1.446224854011234] <- {Rule[x, 1], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5538873165522964, 1.446224854011234] <- {Rule[x, 2], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.564006559795544, 1.446224854011234] <- {Rule[x, 3], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.4528910462808704, -1.446224854011234] <- {Rule[x, 1], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5538873165522964, -1.446224854011234] <- {Rule[x, 2], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.564006559795544, -1.446224854011234] <- {Rule[x, 3], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/9.8.E11 9.8.E11] || [[Item:Q2843|<math>\Airyphasetheta@{x} = \tfrac{2}{3}\pi+\atan@{\BesselY{1/3}@{\xi}/\BesselJ{1/3}@{\xi}}</math>]] || <code>arctan(AiryAi(x)/AiryBi(x))=(2)/(3)*Pi + arctan(BesselY(1/ 3, xi)/ BesselJ(1/ 3, xi))</code> || <code>ArcTan[Divide[AiryAi[x], AiryBi[x]]]=Divide[2,3]*Pi + ArcTan[BesselY[1/ 3, \[Xi]]/ BesselJ[1/ 3, \[Xi]]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-2.062235934-1.435552558*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-2.163232204-1.435552558*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-2.173351447-1.435552558*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.062235934+1.435552558*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-2.062235934109286, -1.435552557338311] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.163232204380712, -1.435552557338311] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.17335144762396, -1.435552557338311] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.062235934109286, 1.435552557338311] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
| [https://dlmf.nist.gov/9.8.E12 9.8.E12] || [[Item:Q2844|<math>\Airyphasederivphi@{x} = \tfrac{1}{3}\pi+\atan@{\BesselY{2/3}@{\xi}/\BesselJ{2/3}@{\xi}}</math>]] || <code>arctan(AiryAi(1, x)/AiryBi(1, x))=(1)/(3)*Pi + arctan(BesselY(2/ 3, xi)/ BesselJ(2/ 3, xi))</code> || <code>ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]=Divide[1,3]*Pi + ArcTan[BesselY[2/ 3, \[Xi]]/ BesselJ[2/ 3, \[Xi]]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.8340487847-1.384157839*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-.6779445534-1.384157839*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.6655182693-1.384157839*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-.8340487847+1.384157839*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-.6779445534+1.384157839*I <- {xi = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.6655182693+1.384157839*I <- {xi = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.043945925+1.377572426*I <- {xi = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-.8878416937+1.377572426*I <- {xi = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.8754154096+1.377572426*I <- {xi = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.043945925-1.377572426*I <- {xi = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-.8878416937-1.377572426*I <- {xi = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.8754154096-1.377572426*I <- {xi = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.8340487867218234, -1.3841578383770126] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6779445554392751, -1.3841578383770126] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6655182713247128, -1.3841578383770126] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8340487867218234, 1.3841578383770126] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6779445554392751, 1.3841578383770126] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6655182713247128, 1.3841578383770126] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0439459252817185, 1.377572426699353] <- {Rule[x, 1], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8878416939991702, 1.377572426699353] <- {Rule[x, 2], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8754154098846079, 1.377572426699353] <- {Rule[x, 3], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0439459252817185, -1.377572426699353] <- {Rule[x, 1], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8878416939991702, -1.377572426699353] <- {Rule[x, 2], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8754154098846079, -1.377572426699353] <- {Rule[x, 3], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/9.8.E12 9.8.E12] || [[Item:Q2844|<math>\Airyphasederivphi@{x} = \tfrac{1}{3}\pi+\atan@{\BesselY{2/3}@{\xi}/\BesselJ{2/3}@{\xi}}</math>]] || <code>arctan(AiryAi(1, x)/AiryBi(1, x))=(1)/(3)*Pi + arctan(BesselY(2/ 3, xi)/ BesselJ(2/ 3, xi))</code> || <code>ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]=Divide[1,3]*Pi + ArcTan[BesselY[2/ 3, \[Xi]]/ BesselJ[2/ 3, \[Xi]]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.8340487847-1.384157839*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-.6779445534-1.384157839*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.6655182693-1.384157839*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-.8340487847+1.384157839*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.8340487867218234, -1.3841578383770126] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6779445554392751, -1.3841578383770126] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6655182713247128, -1.3841578383770126] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8340487867218234, 1.3841578383770126] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
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| [https://dlmf.nist.gov/9.8.E13 9.8.E13] || [[Item:Q2845|<math>\AirymodM@{x}\AirymodderivN@{x}\sin@{\Airyphasetheta@{x}-\Airyphasederivphi@{x}} = \pi^{-1}</math>]] || <code>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)</code> || <code>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)</code> || Failure || Failure || Successful || Successful  
 
| [https://dlmf.nist.gov/9.8.E13 9.8.E13] || [[Item:Q2845|<math>\AirymodM@{x}\AirymodderivN@{x}\sin@{\Airyphasetheta@{x}-\Airyphasederivphi@{x}} = \pi^{-1}</math>]] || <code>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)</code> || <code>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)</code> || Failure || Failure || Successful || Successful  
Line 239: Line 239:
 
| [https://dlmf.nist.gov/9.8.E19 9.8.E19] || [[Item:Q2854|<math>\Airyphasetheta'^{2}@{x}+\tfrac{1}{2}(\Airyphasetheta'''@{x}/\Airyphasetheta'@{x})-\tfrac{3}{4}(\Airyphasetheta''@{x}/\Airyphasetheta'@{x})^{2} = -x</math>]] || <code>(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</code> || <code>((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</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/9.8.E19 9.8.E19] || [[Item:Q2854|<math>\Airyphasetheta'^{2}@{x}+\tfrac{1}{2}(\Airyphasetheta'''@{x}/\Airyphasetheta'@{x})-\tfrac{3}{4}(\Airyphasetheta''@{x}/\Airyphasetheta'@{x})^{2} = -x</math>]] || <code>(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</code> || <code>((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</code> || Successful || Successful || - || -  
 
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| [https://dlmf.nist.gov/9.10.E1 9.10.E1] || [[Item:Q2883|<math>\int_{z}^{\infty}\AiryAi@{t}\diff{t} = \pi\left(\AiryAi@{z}\ScorerGi'@{z}-\AiryAi'@{z}\ScorerGi@{z}\right)</math>]] || <code>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))))</code> || <code>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])</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[Plus[Times[Rational[1, 18], Plus[6, Times[-3, Power[3, Rational[5, 6]], Power[Pi, -1], z, Gamma[Rational[1, 3]], HypergeometricPFQ[{Rational[1, 3]}, {Rational[2, 3], Rational[4, 3]}, Times[Rational[1, 9], Power[z, 3]]]], Times[Power[3, Rational[2, 3]], Power[z, 2], Power[Gamma[Rational[4, 3]], -1], HypergeometricPFQ[{Rational[2, 3]}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], Times[-1, Pi, Plus[Times[-1, AiryAiPrime[z], ScorerGi[z]], Times[AiryAi[z], ScorerGiPrime[z]]]]], And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[Plus[Times[Rational[1, 18], Plus[6, Times[-3, Power[3, Rational[5, 6]], Power[Pi, -1], z, Gamma[Rational[1, 3]], HypergeometricPFQ[{Rational[1, 3]}, {Rational[2, 3], Rational[4, 3]}, Times[Rational[1, 9], Power[z, 3]]]], Times[Power[3, Rational[2, 3]], Power[z, 2], Power[Gamma[Rational[4, 3]], -1], HypergeometricPFQ[{Rational[2, 3]}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], Times[-1, Pi, Plus[Times[-1, AiryAiPrime[z], ScorerGi[z]], Times[AiryAi[z], ScorerGiPrime[z]]]]], And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[Plus[Times[Rational[1, 18], Plus[6, Times[-3, Power[3, Rational[5, 6]], Power[Pi, -1], z, Gamma[Rational[1, 3]], HypergeometricPFQ[{Rational[1, 3]}, {Rational[2, 3], Rational[4, 3]}, Times[Rational[1, 9], Power[z, 3]]]], Times[Power[3, Rational[2, 3]], Power[z, 2], Power[Gamma[Rational[4, 3]], -1], HypergeometricPFQ[{Rational[2, 3]}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], Times[-1, Pi, Plus[Times[-1, AiryAiPrime[z], ScorerGi[z]], Times[AiryAi[z], ScorerGiPrime[z]]]]], And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[Plus[Times[Rational[1, 18], Plus[6, Times[-3, Power[3, Rational[5, 6]], Power[Pi, -1], z, Gamma[Rational[1, 3]], HypergeometricPFQ[{Rational[1, 3]}, {Rational[2, 3], Rational[4, 3]}, Times[Rational[1, 9], Power[z, 3]]]], Times[Power[3, Rational[2, 3]], Power[z, 2], Power[Gamma[Rational[4, 3]], -1], HypergeometricPFQ[{Rational[2, 3]}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], Times[-1, Pi, Plus[Times[-1, AiryAiPrime[z], ScorerGi[z]], Times[AiryAi[z], ScorerGiPrime[z]]]]], And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
+
| [https://dlmf.nist.gov/9.10.E1 9.10.E1] || [[Item:Q2883|<math>\int_{z}^{\infty}\AiryAi@{t}\diff{t} = \pi\left(\AiryAi@{z}\ScorerGi'@{z}-\AiryAi'@{z}\ScorerGi@{z}\right)</math>]] || <code>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))))</code> || <code>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])</code> || Failure || Failure || Skip || Successful
 
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| [https://dlmf.nist.gov/9.10.E2 9.10.E2] || [[Item:Q2884|<math>\int_{-\infty}^{z}\AiryAi@{t}\diff{t} = \pi\left(\AiryAi@{z}\ScorerHi'@{z}-\AiryAi'@{z}\ScorerHi@{z}\right)</math>]] || <code>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))))</code> || <code>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])</code> || Failure || Failure || Skip || Successful  
 
| [https://dlmf.nist.gov/9.10.E2 9.10.E2] || [[Item:Q2884|<math>\int_{-\infty}^{z}\AiryAi@{t}\diff{t} = \pi\left(\AiryAi@{z}\ScorerHi'@{z}-\AiryAi'@{z}\ScorerHi@{z}\right)</math>]] || <code>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))))</code> || <code>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])</code> || Failure || Failure || Skip || Successful  
 
|-
 
|-
| [https://dlmf.nist.gov/9.10.E3 9.10.E3] || [[Item:Q2885|<math>\int_{-\infty}^{z}\AiryBi@{t}\diff{t} = \int_{0}^{z}\AiryBi@{t}\diff{t}</math>]] || <code>int(AiryBi(t), t = - infinity..z)= int(AiryBi(t), t = 0..z)</code> || <code>Integrate[AiryBi[t], {t, - Infinity, z}]= Integrate[AiryBi[t], {t, 0, z}]</code> || Successful || Failure || - || Skip
+
| [https://dlmf.nist.gov/9.10.E3 9.10.E3] || [[Item:Q2885|<math>\int_{-\infty}^{z}\AiryBi@{t}\diff{t} = \int_{0}^{z}\AiryBi@{t}\diff{t}</math>]] || <code>int(AiryBi(t), t = - infinity..z)= int(AiryBi(t), t = 0..z)</code> || <code>Integrate[AiryBi[t], {t, - Infinity, z}]= Integrate[AiryBi[t], {t, 0, z}]</code> || Successful || Failure || - || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/9.10.E3 9.10.E3] || [[Item:Q2885|<math>\pi\left(\AiryBi'@{z}\ScorerGi@{z}-\AiryBi@{z}\ScorerGi'@{z}\right)\\ = \pi\left(\AiryBi@{z}\ScorerHi'@{z}-\AiryBi'@{z}\ScorerHi@{z}\right)</math>]] || <code>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))))</code> || <code>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])</code> || Error || Error || - || -  
 
| [https://dlmf.nist.gov/9.10.E3 9.10.E3] || [[Item:Q2885|<math>\pi\left(\AiryBi'@{z}\ScorerGi@{z}-\AiryBi@{z}\ScorerGi'@{z}\right)\\ = \pi\left(\AiryBi@{z}\ScorerHi'@{z}-\AiryBi'@{z}\ScorerHi@{z}\right)</math>]] || <code>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))))</code> || <code>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])</code> || Error || Error || - || -  
Line 249: Line 249:
 
| [https://dlmf.nist.gov/9.10#Ex1 9.10#Ex1] || [[Item:Q2893|<math>\int_{0}^{\infty}\AiryAi@{t}\diff{t} = \tfrac{1}{3}</math>]] || <code>int(AiryAi(t), t = 0..infinity)=(1)/(3)</code> || <code>Integrate[AiryAi[t], {t, 0, Infinity}]=Divide[1,3]</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/9.10#Ex1 9.10#Ex1] || [[Item:Q2893|<math>\int_{0}^{\infty}\AiryAi@{t}\diff{t} = \tfrac{1}{3}</math>]] || <code>int(AiryAi(t), t = 0..infinity)=(1)/(3)</code> || <code>Integrate[AiryAi[t], {t, 0, Infinity}]=Divide[1,3]</code> || Successful || Successful || - || -  
 
|-
 
|-
| [https://dlmf.nist.gov/9.10#Ex2 9.10#Ex2] || [[Item:Q2894|<math>\int_{-\infty}^{0}\AiryAi@{t}\diff{t} = \tfrac{2}{3}</math>]] || <code>int(AiryAi(t), t = - infinity..0)=(2)/(3)</code> || <code>Integrate[AiryAi[t], {t, - Infinity, 0}]=Divide[2,3]</code> || Successful || Failure || - || Error
+
| [https://dlmf.nist.gov/9.10#Ex2 9.10#Ex2] || [[Item:Q2894|<math>\int_{-\infty}^{0}\AiryAi@{t}\diff{t} = \tfrac{2}{3}</math>]] || <code>int(AiryAi(t), t = - infinity..0)=(2)/(3)</code> || <code>Integrate[AiryAi[t], {t, - Infinity, 0}]=Divide[2,3]</code> || Successful || Failure || - || Successful
 
|-
 
|-
| [https://dlmf.nist.gov/9.10.E12 9.10.E12] || [[Item:Q2895|<math>\int_{-\infty}^{0}\AiryBi@{t}\diff{t} = 0</math>]] || <code>int(AiryBi(t), t = - infinity..0)= 0</code> || <code>Integrate[AiryBi[t], {t, - Infinity, 0}]= 0</code> || Successful || Failure || - || Error
+
| [https://dlmf.nist.gov/9.10.E12 9.10.E12] || [[Item:Q2895|<math>\int_{-\infty}^{0}\AiryBi@{t}\diff{t} = 0</math>]] || <code>int(AiryBi(t), t = - infinity..0)= 0</code> || <code>Integrate[AiryBi[t], {t, - Infinity, 0}]= 0</code> || Successful || Failure || - || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/9.10.E13 9.10.E13] || [[Item:Q2896|<math>\int_{-\infty}^{\infty}e^{pt}\AiryAi@{t}\diff{t} = e^{p^{3}/3}</math>]] || <code>int(exp(p*t)*AiryAi(t), t = - infinity..infinity)= exp((p)^(3)/ 3)</code> || <code>Integrate[Exp[p*t]*AiryAi[t], {t, - Infinity, Infinity}]= Exp[(p)^(3)/ 3]</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/9.10.E13 9.10.E13] || [[Item:Q2896|<math>\int_{-\infty}^{\infty}e^{pt}\AiryAi@{t}\diff{t} = e^{p^{3}/3}</math>]] || <code>int(exp(p*t)*AiryAi(t), t = - infinity..infinity)= exp((p)^(3)/ 3)</code> || <code>Integrate[Exp[p*t]*AiryAi[t], {t, - Infinity, Infinity}]= Exp[(p)^(3)/ 3]</code> || Failure || Failure || Skip || Error  
 
|-
 
|-
| [https://dlmf.nist.gov/9.10.E14 9.10.E14] || [[Item:Q2897|<math>\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)</math>]] || <code>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))))</code> || <code>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]]])</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[p, Complex[1, 1]], Rule[ConditionalExpression[Plus[Times[Rational[1, 6], Power[E, Times[Rational[-1, 3], Power[p, 3]]], Power[p, -2], Power[Pi, -1], Plus[Times[2, Plus[Power[p, 2], Times[-1, p, Power[Times[-1, Power[p, 3]], Rational[1, 3]]], Power[Times[-1, Power[p, 3]], Rational[2, 3]]], Pi], Times[-1, Power[3, Rational[-1, 6]], Power[p, 4], ExpIntegralE[Rational[1, 3], Times[Rational[-1, 3], Power[p, 3]]], Gamma[Rational[1, 3]]], Times[Power[3, Rational[1, 6]], Power[p, 3], ExpIntegralE[Rational[2, 3], Times[Rational[-1, 3], Power[p, 3]]], Gamma[Rational[2, 3]]]]], Times[-1, Power[E, Times[Rational[-1, 3], Power[p, 3]]], Plus[Rational[1, 3], Times[Rational[-1, 9], p, Power[Times[-1, Power[p, 3]], Rational[-1, 3]], Power[Gamma[Rational[4, 3]], -1], Gamma[Rational[1, 3], 0, Times[Rational[-1, 3], Power[p, 3]]]], Times[Rational[2, 9], Power[p, 2], Power[Times[-1, Power[p, 3]], Rational[-2, 3]], Power[Gamma[Rational[5, 3]], -1], Gamma[Rational[2, 3], 0, Times[Rational[-1, 3], Power[p, 3]]]]]]], Greater[Re[p], 0]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[p, Complex[1, 1]], Rule[ConditionalExpression[Plus[Times[Rational[1, 6], Power[E, Times[Rational[-1, 3], Power[p, 3]]], Power[p, -2], Power[Pi, -1], Plus[Times[2, Plus[Power[p, 2], Times[-1, p, Power[Times[-1, Power[p, 3]], Rational[1, 3]]], Power[Times[-1, Power[p, 3]], Rational[2, 3]]], Pi], Times[-1, Power[3, Rational[-1, 6]], Power[p, 4], ExpIntegralE[Rational[1, 3], Times[Rational[-1, 3], Power[p, 3]]], Gamma[Rational[1, 3]]], Times[Power[3, Rational[1, 6]], Power[p, 3], ExpIntegralE[Rational[2, 3], Times[Rational[-1, 3], Power[p, 3]]], Gamma[Rational[2, 3]]]]], Times[-1, Power[E, Times[Rational[-1, 3], Power[p, 3]]], Plus[Rational[1, 3], Times[Rational[-1, 9], p, Power[Times[-1, Power[p, 3]], Rational[-1, 3]], Power[Gamma[Rational[4, 3]], -1], Gamma[Rational[1, 3], 0, Times[Rational[-1, 3], Power[p, 3]]]], Times[Rational[2, 9], Power[p, 2], Power[Times[-1, Power[p, 3]], Rational[-2, 3]], Power[Gamma[Rational[5, 3]], -1], Gamma[Rational[2, 3], 0, Times[Rational[-1, 3], Power[p, 3]]]]]]], Greater[Re[p], 0]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[p, Complex[1, 1]], Rule[ConditionalExpression[Plus[Times[Rational[1, 6], Power[E, Times[Rational[-1, 3], Power[p, 3]]], Power[p, -2], Power[Pi, -1], Plus[Times[2, Plus[Power[p, 2], Times[-1, p, Power[Times[-1, Power[p, 3]], Rational[1, 3]]], Power[Times[-1, Power[p, 3]], Rational[2, 3]]], Pi], Times[-1, Power[3, Rational[-1, 6]], Power[p, 4], ExpIntegralE[Rational[1, 3], Times[Rational[-1, 3], Power[p, 3]]], Gamma[Rational[1, 3]]], Times[Power[3, Rational[1, 6]], Power[p, 3], ExpIntegralE[Rational[2, 3], Times[Rational[-1, 3], Power[p, 3]]], Gamma[Rational[2, 3]]]]], Times[-1, Power[E, Times[Rational[-1, 3], Power[p, 3]]], Plus[Rational[1, 3], Times[Rational[-1, 9], p, Power[Times[-1, Power[p, 3]], Rational[-1, 3]], Power[Gamma[Rational[4, 3]], -1], Gamma[Rational[1, 3], 0, Times[Rational[-1, 3], Power[p, 3]]]], Times[Rational[2, 9], Power[p, 2], Power[Times[-1, Power[p, 3]], Rational[-2, 3]], Power[Gamma[Rational[5, 3]], -1], Gamma[Rational[2, 3], 0, Times[Rational[-1, 3], Power[p, 3]]]]]]], Greater[Re[p], 0]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[p, Complex[1, 1]], Rule[ConditionalExpression[Plus[Times[Rational[1, 6], Power[E, Times[Rational[-1, 3], Power[p, 3]]], Power[p, -2], Power[Pi, -1], Plus[Times[2, Plus[Power[p, 2], Times[-1, p, Power[Times[-1, Power[p, 3]], Rational[1, 3]]], Power[Times[-1, Power[p, 3]], Rational[2, 3]]], Pi], Times[-1, Power[3, Rational[-1, 6]], Power[p, 4], ExpIntegralE[Rational[1, 3], Times[Rational[-1, 3], Power[p, 3]]], Gamma[Rational[1, 3]]], Times[Power[3, Rational[1, 6]], Power[p, 3], ExpIntegralE[Rational[2, 3], Times[Rational[-1, 3], Power[p, 3]]], Gamma[Rational[2, 3]]]]], Times[-1, Power[E, Times[Rational[-1, 3], Power[p, 3]]], Plus[Rational[1, 3], Times[Rational[-1, 9], p, Power[Times[-1, Power[p, 3]], Rational[-1, 3]], Power[Gamma[Rational[4, 3]], -1], Gamma[Rational[1, 3], 0, Times[Rational[-1, 3], Power[p, 3]]]], Times[Rational[2, 9], Power[p, 2], Power[Times[-1, Power[p, 3]], Rational[-2, 3]], Power[Gamma[Rational[5, 3]], -1], Gamma[Rational[2, 3], 0, Times[Rational[-1, 3], Power[p, 3]]]]]]], Greater[Re[p], 0]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
+
| [https://dlmf.nist.gov/9.10.E14 9.10.E14] || [[Item:Q2897|<math>\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)</math>]] || <code>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))))</code> || <code>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]]])</code> || Successful || Failure || - || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/9.10.E15 9.10.E15] || [[Item:Q2898|<math>\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)}</math>]] || <code>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))))</code> || <code>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]]])</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/9.10.E15 9.10.E15] || [[Item:Q2898|<math>\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)}</math>]] || <code>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))))</code> || <code>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]]])</code> || Failure || Failure || Skip || Error  
Line 265: Line 265:
 
| [https://dlmf.nist.gov/9.10#Ex3 9.10#Ex3] || [[Item:Q2902|<math>\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}</math>]] || <code>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)</code> || <code>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}]</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/9.10#Ex3 9.10#Ex3] || [[Item:Q2902|<math>\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}</math>]] || <code>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)</code> || <code>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}]</code> || Failure || Failure || Skip || Error  
 
|-
 
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| [https://dlmf.nist.gov/9.10.E20 9.10.E20] || [[Item:Q2905|<math>\int_{0}^{x}\!\!\int_{0}^{v}\AiryAi@{t}\diff{t}\diff{v} = x\int_{0}^{x}\AiryAi@{t}\diff{t}-\AiryAi'@{x}+\AiryAi'@{0}</math>]] || <code>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) ) )</code> || <code>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)</code> || Failure || Failure || Skip || Skip
+
| [https://dlmf.nist.gov/9.10.E20 9.10.E20] || [[Item:Q2905|<math>\int_{0}^{x}\!\!\int_{0}^{v}\AiryAi@{t}\diff{t}\diff{v} = x\int_{0}^{x}\AiryAi@{t}\diff{t}-\AiryAi'@{x}+\AiryAi'@{0}</math>]] || <code>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) ) )</code> || <code>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)</code> || Failure || Failure || Skip || Successful
 
|-
 
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| [https://dlmf.nist.gov/9.10.E21 9.10.E21] || [[Item:Q2906|<math>\int_{0}^{x}\!\!\int_{0}^{v}\AiryBi@{t}\diff{t}\diff{v} = x\int_{0}^{x}\AiryBi@{t}\diff{t}-\AiryBi'@{x}+\AiryBi'@{0}</math>]] || <code>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) ) )</code> || <code>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)</code> || Failure || Failure || Skip || Successful  
 
| [https://dlmf.nist.gov/9.10.E21 9.10.E21] || [[Item:Q2906|<math>\int_{0}^{x}\!\!\int_{0}^{v}\AiryBi@{t}\diff{t}\diff{v} = x\int_{0}^{x}\AiryBi@{t}\diff{t}-\AiryBi'@{x}+\AiryBi'@{0}</math>]] || <code>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) ) )</code> || <code>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)</code> || Failure || Failure || Skip || Successful  
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| [https://dlmf.nist.gov/9.11.E3 9.11.E3] || [[Item:Q2910|<math>\AiryAi^{2}@{x} = \frac{1}{4\pi\sqrt{3}}\int_{0}^{\infty}\BesselJ{0}@{\tfrac{1}{12}t^{3}+xt}t\diff{t}</math>]] || <code>(AiryAi(x))^(2)=(1)/(4*Pi*sqrt(3))*int(BesselJ(0, (1)/(12)*(t)^(3)+ x*t)*t, t = 0..infinity)</code> || <code>(AiryAi[x])^(2)=Divide[1,4*Pi*Sqrt[3]]*Integrate[BesselJ[0, Divide[1,12]*(t)^(3)+ x*t]*t, {t, 0, Infinity}]</code> || Failure || Failure || Skip || Skip  
 
| [https://dlmf.nist.gov/9.11.E3 9.11.E3] || [[Item:Q2910|<math>\AiryAi^{2}@{x} = \frac{1}{4\pi\sqrt{3}}\int_{0}^{\infty}\BesselJ{0}@{\tfrac{1}{12}t^{3}+xt}t\diff{t}</math>]] || <code>(AiryAi(x))^(2)=(1)/(4*Pi*sqrt(3))*int(BesselJ(0, (1)/(12)*(t)^(3)+ x*t)*t, t = 0..infinity)</code> || <code>(AiryAi[x])^(2)=Divide[1,4*Pi*Sqrt[3]]*Integrate[BesselJ[0, Divide[1,12]*(t)^(3)+ x*t]*t, {t, 0, Infinity}]</code> || Failure || Failure || Skip || Skip  
 
|-
 
|-
| [https://dlmf.nist.gov/9.11.E4 9.11.E4] || [[Item:Q2911|<math>\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}</math>]] || <code>(AiryAi(z))^(2)+ (AiryBi(z))^(2)=(1)/((Pi)^(3/ 2))*int(exp(z*t -(1)/(12)*(t)^(3))*(t)^(- 1/ 2), t = 0..infinity)</code> || <code>(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}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[0, Less[Re[z], 0]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[0, Less[Re[z], 0]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[0, Less[Re[z], 0]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[0, Less[Re[z], 0]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
+
| [https://dlmf.nist.gov/9.11.E4 9.11.E4] || [[Item:Q2911|<math>\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}</math>]] || <code>(AiryAi(z))^(2)+ (AiryBi(z))^(2)=(1)/((Pi)^(3/ 2))*int(exp(z*t -(1)/(12)*(t)^(3))*(t)^(- 1/ 2), t = 0..infinity)</code> || <code>(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}]</code> || Failure || Failure || Skip || Successful
 
|-
 
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| [https://dlmf.nist.gov/9.11.E12 9.11.E12] || [[Item:Q2919|<math>\int\frac{\diff{z}}{\AiryAi^{2}@{z}} = \pi\frac{\AiryBi@{z}}{\AiryAi@{z}}</math>]] || <code>int((1)/((AiryAi(z))^(2)), z)= Pi*(AiryBi(z))/(AiryAi(z))</code> || <code>Integrate[Divide[1,(AiryAi[z])^(2)], z]= Pi*Divide[AiryBi[z],AiryAi[z]]</code> || Failure || Successful || Skip || -  
 
| [https://dlmf.nist.gov/9.11.E12 9.11.E12] || [[Item:Q2919|<math>\int\frac{\diff{z}}{\AiryAi^{2}@{z}} = \pi\frac{\AiryBi@{z}}{\AiryAi@{z}}</math>]] || <code>int((1)/((AiryAi(z))^(2)), z)= Pi*(AiryBi(z))/(AiryAi(z))</code> || <code>Integrate[Divide[1,(AiryAi[z])^(2)], z]= Pi*Divide[AiryBi[z],AiryAi[z]]</code> || Failure || Successful || Skip || -  
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| [https://dlmf.nist.gov/9.11.E14 9.11.E14] || [[Item:Q2921|<math>\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}}</math>]] || <code>int((AiryAi(z)*AiryBi(z))/(((AiryAi(z))^(2)+ (AiryBi(z))^(2))^(2)), z)=(Pi)/(2)*((AiryBi(z))^(2))/((AiryAi(z))^(2)+ (AiryBi(z))^(2))</code> || <code>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)]</code> || Failure || Failure || Skip || Successful  
 
| [https://dlmf.nist.gov/9.11.E14 9.11.E14] || [[Item:Q2921|<math>\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}}</math>]] || <code>int((AiryAi(z)*AiryBi(z))/(((AiryAi(z))^(2)+ (AiryBi(z))^(2))^(2)), z)=(Pi)/(2)*((AiryBi(z))^(2))/((AiryAi(z))^(2)+ (AiryBi(z))^(2))</code> || <code>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)]</code> || Failure || Failure || Skip || Successful  
 
|-
 
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| [https://dlmf.nist.gov/9.11.E15 9.11.E15] || [[Item:Q2922|<math>\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}}}</math>]] || <code>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)))</code> || <code>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]]]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[α, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[-1, Power[2, Plus[1, Times[Rational[1, 3], Plus[-5, Times[-2, α]]]]], Power[3, Times[Rational[1, 6], Plus[-5, Times[-2, α]]]], Power[Pi, Rational[-1, 2]], Power[Gamma[Plus[Rational[5, 6], Times[Rational[1, 3], α]]], -1], Gamma[α]], Times[Power[2, Plus[Rational[-5, 3], Times[Rational[-2, 3], α]]], Power[3, Plus[Rational[-11, 6], Times[Rational[-1, 3], α]]], Power[Pi, Rational[-3, 2]], Gamma[Plus[Rational[1, 6], Times[Rational[-1, 3], α]]], Power[Gamma[Plus[Rational[1, 3], Times[Rational[-1, 3], α]]], -1], Plus[Times[Power[3, α], Gamma[Times[Rational[1, 3], α]], Gamma[Times[Rational[1, 3], Plus[1, α]]]], Times[-2, Power[3, Rational[1, 2]], Gamma[Plus[Rational[1, 3], Times[Rational[-1, 3], α]]], Gamma[α], Sin[Times[Rational[1, 3], Pi, α]]]]]], Greater[Re[α], 0]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[α, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[-1, Power[2, Plus[1, Times[Rational[1, 3], Plus[-5, Times[-2, α]]]]], Power[3, Times[Rational[1, 6], Plus[-5, Times[-2, α]]]], Power[Pi, Rational[-1, 2]], Power[Gamma[Plus[Rational[5, 6], Times[Rational[1, 3], α]]], -1], Gamma[α]], Times[Power[2, Plus[Rational[-5, 3], Times[Rational[-2, 3], α]]], Power[3, Plus[Rational[-11, 6], Times[Rational[-1, 3], α]]], Power[Pi, Rational[-3, 2]], Gamma[Plus[Rational[1, 6], Times[Rational[-1, 3], α]]], Power[Gamma[Plus[Rational[1, 3], Times[Rational[-1, 3], α]]], -1], Plus[Times[Power[3, α], Gamma[Times[Rational[1, 3], α]], Gamma[Times[Rational[1, 3], Plus[1, α]]]], Times[-2, Power[3, Rational[1, 2]], Gamma[Plus[Rational[1, 3], Times[Rational[-1, 3], α]]], Gamma[α], Sin[Times[Rational[1, 3], Pi, α]]]]]], Greater[Re[α], 0]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[α, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[-1, Power[2, Plus[1, Times[Rational[1, 3], Plus[-5, Times[-2, α]]]]], Power[3, Times[Rational[1, 6], Plus[-5, Times[-2, α]]]], Power[Pi, Rational[-1, 2]], Power[Gamma[Plus[Rational[5, 6], Times[Rational[1, 3], α]]], -1], Gamma[α]], Times[Power[2, Plus[Rational[-5, 3], Times[Rational[-2, 3], α]]], Power[3, Plus[Rational[-11, 6], Times[Rational[-1, 3], α]]], Power[Pi, Rational[-3, 2]], Gamma[Plus[Rational[1, 6], Times[Rational[-1, 3], α]]], Power[Gamma[Plus[Rational[1, 3], Times[Rational[-1, 3], α]]], -1], Plus[Times[Power[3, α], Gamma[Times[Rational[1, 3], α]], Gamma[Times[Rational[1, 3], Plus[1, α]]]], Times[-2, Power[3, Rational[1, 2]], Gamma[Plus[Rational[1, 3], Times[Rational[-1, 3], α]]], Gamma[α], Sin[Times[Rational[1, 3], Pi, α]]]]]], Greater[Re[α], 0]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[α, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[-1, Power[2, Plus[1, Times[Rational[1, 3], Plus[-5, Times[-2, α]]]]], Power[3, Times[Rational[1, 6], Plus[-5, Times[-2, α]]]], Power[Pi, Rational[-1, 2]], Power[Gamma[Plus[Rational[5, 6], Times[Rational[1, 3], α]]], -1], Gamma[α]], Times[Power[2, Plus[Rational[-5, 3], Times[Rational[-2, 3], α]]], Power[3, Plus[Rational[-11, 6], Times[Rational[-1, 3], α]]], Power[Pi, Rational[-3, 2]], Gamma[Plus[Rational[1, 6], Times[Rational[-1, 3], α]]], Power[Gamma[Plus[Rational[1, 3], Times[Rational[-1, 3], α]]], -1], Plus[Times[Power[3, α], Gamma[Times[Rational[1, 3], α]], Gamma[Times[Rational[1, 3], Plus[1, α]]]], Times[-2, Power[3, Rational[1, 2]], Gamma[Plus[Rational[1, 3], Times[Rational[-1, 3], α]]], Gamma[α], Sin[Times[Rational[1, 3], Pi, α]]]]]], Greater[Re[α], 0]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
+
| [https://dlmf.nist.gov/9.11.E15 9.11.E15] || [[Item:Q2922|<math>\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}}}</math>]] || <code>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)))</code> || <code>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]]]</code> || Failure || Failure || Skip || Successful
 
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| [https://dlmf.nist.gov/9.11.E16 9.11.E16] || [[Item:Q2923|<math>\int_{-\infty}^{\infty}\AiryAi^{3}@{t}\diff{t} = \frac{\EulerGamma^{2}@{\frac{1}{3}}}{4\pi^{2}}</math>]] || <code>int((AiryAi(t))^(3), t = - infinity..infinity)=((GAMMA((1)/(3)))^(2))/(4*(Pi)^(2))</code> || <code>Integrate[(AiryAi[t])^(3), {t, - Infinity, Infinity}]=Divide[(Gamma[Divide[1,3]])^(2),4*(Pi)^(2)]</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/9.11.E16 9.11.E16] || [[Item:Q2923|<math>\int_{-\infty}^{\infty}\AiryAi^{3}@{t}\diff{t} = \frac{\EulerGamma^{2}@{\frac{1}{3}}}{4\pi^{2}}</math>]] || <code>int((AiryAi(t))^(3), t = - infinity..infinity)=((GAMMA((1)/(3)))^(2))/(4*(Pi)^(2))</code> || <code>Integrate[(AiryAi[t])^(3), {t, - Infinity, Infinity}]=Divide[(Gamma[Divide[1,3]])^(2),4*(Pi)^(2)]</code> || Failure || Failure || Skip || Error  
Line 293: Line 293:
 
| [https://dlmf.nist.gov/9.11.E19 9.11.E19] || [[Item:Q2926|<math>\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}}</math>]] || <code>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)</code> || <code>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}]</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/9.11.E19 9.11.E19] || [[Item:Q2926|<math>\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}}</math>]] || <code>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)</code> || <code>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}]</code> || Failure || Failure || Skip || Error  
 
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| [https://dlmf.nist.gov/9.11.E19 9.11.E19] || [[Item:Q2926|<math>\int_{0}^{\infty}\frac{t\diff{t}}{\AiryAi'^{2}@{t}+\AiryBi'^{2}@{t}} = \frac{\pi^{2}}{6}</math>]] || <code>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)</code> || <code>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]</code> || Failure || Failure || Skip || Error
+
| [https://dlmf.nist.gov/9.11.E19 9.11.E19] || [[Item:Q2926|<math>\int_{0}^{\infty}\frac{t\diff{t}}{\AiryAi'^{2}@{t}+\AiryBi'^{2}@{t}} = \frac{\pi^{2}}{6}</math>]] || <code>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)</code> || <code>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]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>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]]]]}</code><br><code>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]]]]}</code><br><code>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]]]]}</code><br><code>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]]]]}</code><br></div></div>
 
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| [https://dlmf.nist.gov/9.12.E1 9.12.E1] || [[Item:Q2927|<math>\deriv[2]{w}{z}-zw = \frac{1}{\pi}</math>]] || <code>diff(w, [z$(2)])- z*w =(1)/(Pi)</code> || <code>D[w, {z, 2}]- z*w =Divide[1,Pi]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.3183098861-3.999999998*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-4.318309884-0.*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-.3183098861+3.999999998*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>3.681690112-0.*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-4.318309884-0.*I <- {w = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.3183098861+3.999999998*I <- {w = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>3.681690112-0.*I <- {w = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.3183098861-3.999999998*I <- {w = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-.3183098861+3.999999998*I <- {w = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>3.681690112-0.*I <- {w = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-.3183098861-3.999999998*I <- {w = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-4.318309884-0.*I <- {w = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>3.681690112-0.*I <- {w = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.3183098861-3.999999998*I <- {w = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-4.318309884-0.*I <- {w = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.3183098861+3.999999998*I <- {w = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || Error  
+
| [https://dlmf.nist.gov/9.12.E1 9.12.E1] || [[Item:Q2927|<math>\deriv[2]{w}{z}-zw = \frac{1}{\pi}</math>]] || <code>diff(w, [z$(2)])- z*w =(1)/(Pi)</code> || <code>D[w, {z, 2}]- z*w =Divide[1,Pi]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.3183098861-3.999999998*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-4.318309884-0.*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-.3183098861+3.999999998*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>3.681690112-0.*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Error  
 
|-
 
|-
| [https://dlmf.nist.gov/9.12.E4 9.12.E4] || [[Item:Q2932|<math>\ScorerGi@{z} = \AiryBi@{z}\int_{z}^{\infty}\AiryAi@{t}\diff{t}+\AiryAi@{z}\int_{0}^{z}\AiryBi@{t}\diff{t}</math>]] || <code>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)</code> || <code>ScorerGi[z]= AiryBi[z]*Integrate[AiryAi[t], {t, z, Infinity}]+ AiryAi[z]*Integrate[AiryBi[t], {t, 0, z}]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[Plus[Times[-1, AiryAi[z], Plus[Times[Power[3, Rational[-1, 6]], z, Power[Gamma[Rational[2, 3]], -1], HypergeometricPFQ[{Rational[1, 3]}, {Rational[2, 3], Rational[4, 3]}, Times[Rational[1, 9], Power[z, 3]]]], Times[Rational[-1, 4], Power[3, Rational[-1, 3]], Power[Pi, -1], Power[z, 2], Gamma[Rational[-1, 3]], HypergeometricPFQ[{Rational[2, 3]}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], Times[Rational[-1, 18], AiryBi[z], Plus[6, Times[-3, Power[3, Rational[5, 6]], Power[Pi, -1], z, Gamma[Rational[1, 3]], HypergeometricPFQ[{Rational[1, 3]}, {Rational[2, 3], Rational[4, 3]}, Times[Rational[1, 9], Power[z, 3]]]], Times[Power[3, Rational[2, 3]], Power[z, 2], Power[Gamma[Rational[4, 3]], -1], HypergeometricPFQ[{Rational[2, 3]}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], ScorerGi[z]], And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[Plus[Times[-1, AiryAi[z], Plus[Times[Power[3, Rational[-1, 6]], z, Power[Gamma[Rational[2, 3]], -1], HypergeometricPFQ[{Rational[1, 3]}, {Rational[2, 3], Rational[4, 3]}, Times[Rational[1, 9], Power[z, 3]]]], Times[Rational[-1, 4], Power[3, Rational[-1, 3]], Power[Pi, -1], Power[z, 2], Gamma[Rational[-1, 3]], HypergeometricPFQ[{Rational[2, 3]}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], Times[Rational[-1, 18], AiryBi[z], Plus[6, Times[-3, Power[3, Rational[5, 6]], Power[Pi, -1], z, Gamma[Rational[1, 3]], HypergeometricPFQ[{Rational[1, 3]}, {Rational[2, 3], Rational[4, 3]}, Times[Rational[1, 9], Power[z, 3]]]], Times[Power[3, Rational[2, 3]], Power[z, 2], Power[Gamma[Rational[4, 3]], -1], HypergeometricPFQ[{Rational[2, 3]}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], ScorerGi[z]], And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[Plus[Times[-1, AiryAi[z], Plus[Times[Power[3, Rational[-1, 6]], z, Power[Gamma[Rational[2, 3]], -1], HypergeometricPFQ[{Rational[1, 3]}, {Rational[2, 3], Rational[4, 3]}, Times[Rational[1, 9], Power[z, 3]]]], Times[Rational[-1, 4], Power[3, Rational[-1, 3]], Power[Pi, -1], Power[z, 2], Gamma[Rational[-1, 3]], HypergeometricPFQ[{Rational[2, 3]}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], Times[Rational[-1, 18], AiryBi[z], Plus[6, Times[-3, Power[3, Rational[5, 6]], Power[Pi, -1], z, Gamma[Rational[1, 3]], HypergeometricPFQ[{Rational[1, 3]}, {Rational[2, 3], Rational[4, 3]}, Times[Rational[1, 9], Power[z, 3]]]], Times[Power[3, Rational[2, 3]], Power[z, 2], Power[Gamma[Rational[4, 3]], -1], HypergeometricPFQ[{Rational[2, 3]}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], ScorerGi[z]], And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[Plus[Times[-1, AiryAi[z], Plus[Times[Power[3, Rational[-1, 6]], z, Power[Gamma[Rational[2, 3]], -1], HypergeometricPFQ[{Rational[1, 3]}, {Rational[2, 3], Rational[4, 3]}, Times[Rational[1, 9], Power[z, 3]]]], Times[Rational[-1, 4], Power[3, Rational[-1, 3]], Power[Pi, -1], Power[z, 2], Gamma[Rational[-1, 3]], HypergeometricPFQ[{Rational[2, 3]}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], Times[Rational[-1, 18], AiryBi[z], Plus[6, Times[-3, Power[3, Rational[5, 6]], Power[Pi, -1], z, Gamma[Rational[1, 3]], HypergeometricPFQ[{Rational[1, 3]}, {Rational[2, 3], Rational[4, 3]}, Times[Rational[1, 9], Power[z, 3]]]], Times[Power[3, Rational[2, 3]], Power[z, 2], Power[Gamma[Rational[4, 3]], -1], HypergeometricPFQ[{Rational[2, 3]}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], ScorerGi[z]], And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
+
| [https://dlmf.nist.gov/9.12.E4 9.12.E4] || [[Item:Q2932|<math>\ScorerGi@{z} = \AiryBi@{z}\int_{z}^{\infty}\AiryAi@{t}\diff{t}+\AiryAi@{z}\int_{0}^{z}\AiryBi@{t}\diff{t}</math>]] || <code>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)</code> || <code>ScorerGi[z]= AiryBi[z]*Integrate[AiryAi[t], {t, z, Infinity}]+ AiryAi[z]*Integrate[AiryBi[t], {t, 0, z}]</code> || Successful || Failure || - || Successful
 
|-
 
|-
| [https://dlmf.nist.gov/9.12.E5 9.12.E5] || [[Item:Q2933|<math>\ScorerHi@{z} = \AiryBi@{z}\int_{-\infty}^{z}\AiryAi@{t}\diff{t}-\AiryAi@{z}\int_{-\infty}^{z}\AiryBi@{t}\diff{t}</math>]] || <code>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)</code> || <code>ScorerHi[z]= AiryBi[z]*Integrate[AiryAi[t], {t, - Infinity, z}]- AiryAi[z]*Integrate[AiryBi[t], {t, - Infinity, z}]</code> || Successful || Failure || - || Error
+
| [https://dlmf.nist.gov/9.12.E5 9.12.E5] || [[Item:Q2933|<math>\ScorerHi@{z} = \AiryBi@{z}\int_{-\infty}^{z}\AiryAi@{t}\diff{t}-\AiryAi@{z}\int_{-\infty}^{z}\AiryBi@{t}\diff{t}</math>]] || <code>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)</code> || <code>ScorerHi[z]= AiryBi[z]*Integrate[AiryAi[t], {t, - Infinity, z}]- AiryAi[z]*Integrate[AiryBi[t], {t, - Infinity, z}]</code> || Successful || Failure || - || Skip
 
|-
 
|-
 
| [https://dlmf.nist.gov/9.12.E6 9.12.E6] || [[Item:Q2934|<math>\ScorerGi@{0} = \tfrac{1}{2}\ScorerHi@{0}</math>]] || <code>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)))</code> || <code>ScorerGi[0]=Divide[1,2]*ScorerHi[0]</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/9.12.E6 9.12.E6] || [[Item:Q2934|<math>\ScorerGi@{0} = \tfrac{1}{2}\ScorerHi@{0}</math>]] || <code>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)))</code> || <code>ScorerGi[0]=Divide[1,2]*ScorerHi[0]</code> || Successful || Successful || - || -  
Line 331: Line 331:
 
| [https://dlmf.nist.gov/9.12.E18 9.12.E18] || [[Item:Q2946|<math>\ScorerHi'@{z} = \frac{3^{-1/3}}{\pi}\sum_{k=0}^{\infty}\EulerGamma@{\frac{k+2}{3}}\frac{(3^{1/3}z)^{k}}{k!}</math>]] || <code>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)</code> || <code>(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}]</code> || Failure || Successful || Skip || -  
 
| [https://dlmf.nist.gov/9.12.E18 9.12.E18] || [[Item:Q2946|<math>\ScorerHi'@{z} = \frac{3^{-1/3}}{\pi}\sum_{k=0}^{\infty}\EulerGamma@{\frac{k+2}{3}}\frac{(3^{1/3}z)^{k}}{k!}</math>]] || <code>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)</code> || <code>(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}]</code> || Failure || Successful || Skip || -  
 
|-
 
|-
| [https://dlmf.nist.gov/9.12.E19 9.12.E19] || [[Item:Q2947|<math>\ScorerGi@{x} = \frac{1}{\pi}\int_{0}^{\infty}\sin@{\tfrac{1}{3}t^{3}+xt}\diff{t}</math>]] || <code>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)</code> || <code>ScorerGi[x]=Divide[1,Pi]*Integrate[Sin[Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}]</code> || Failure || Failure || Skip || Skip
+
| [https://dlmf.nist.gov/9.12.E19 9.12.E19] || [[Item:Q2947|<math>\ScorerGi@{x} = \frac{1}{\pi}\int_{0}^{\infty}\sin@{\tfrac{1}{3}t^{3}+xt}\diff{t}</math>]] || <code>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)</code> || <code>ScorerGi[x]=Divide[1,Pi]*Integrate[Sin[Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}]</code> || Failure || Failure || Skip || Successful
 
|-
 
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| [https://dlmf.nist.gov/9.12.E20 9.12.E20] || [[Item:Q2948|<math>\ScorerHi@{z} = \frac{1}{\pi}\int_{0}^{\infty}\exp@{-\tfrac{1}{3}t^{3}+zt}\diff{t}</math>]] || <code>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)</code> || <code>ScorerHi[z]=Divide[1,Pi]*Integrate[Exp[-Divide[1,3]*(t)^(3)+ z*t], {t, 0, Infinity}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[Plus[Times[Rational[-1, 6], Power[Pi, -1], Plus[Times[4, Pi, AiryBi[z]], Times[3, Power[z, 2], HypergeometricPFQ[{1}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], ScorerHi[z]], Less[Re[z], 0]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[Plus[Times[Rational[-1, 6], Power[Pi, -1], Plus[Times[4, Pi, AiryBi[z]], Times[3, Power[z, 2], HypergeometricPFQ[{1}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], ScorerHi[z]], Less[Re[z], 0]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[Plus[Times[Rational[-1, 6], Power[Pi, -1], Plus[Times[4, Pi, AiryBi[z]], Times[3, Power[z, 2], HypergeometricPFQ[{1}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], ScorerHi[z]], Less[Re[z], 0]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[Plus[Times[Rational[-1, 6], Power[Pi, -1], Plus[Times[4, Pi, AiryBi[z]], Times[3, Power[z, 2], HypergeometricPFQ[{1}, {Rational[4, 3], Rational[5, 3]}, Times[Rational[1, 9], Power[z, 3]]]]]], ScorerHi[z]], Less[Re[z], 0]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
+
| [https://dlmf.nist.gov/9.12.E20 9.12.E20] || [[Item:Q2948|<math>\ScorerHi@{z} = \frac{1}{\pi}\int_{0}^{\infty}\exp@{-\tfrac{1}{3}t^{3}+zt}\diff{t}</math>]] || <code>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)</code> || <code>ScorerHi[z]=Divide[1,Pi]*Integrate[Exp[-Divide[1,3]*(t)^(3)+ z*t], {t, 0, Infinity}]</code> || Failure || Failure || Skip || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/9.12.E21 9.12.E21] || [[Item:Q2949|<math>\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}</math>]] || <code>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)</code> || <code>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}]</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/9.12.E21 9.12.E21] || [[Item:Q2949|<math>\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}</math>]] || <code>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)</code> || <code>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}]</code> || Failure || Failure || Skip || Error  
 
|-
 
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| [https://dlmf.nist.gov/9.12.E22 9.12.E22] || [[Item:Q2950|<math>\ScorerHi@{-z} = \frac{4z^{2}}{3^{3/2}\pi^{2}}\int_{0}^{\infty}\frac{\modBesselK{1/3}@{t}}{\zeta^{2}+t^{2}}\diff{t}</math>]] || <code>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)</code> || <code>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}]</code> || Failure || Failure || Skip || Successful
+
| [https://dlmf.nist.gov/9.12.E22 9.12.E22] || [[Item:Q2950|<math>\ScorerHi@{-z} = \frac{4z^{2}}{3^{3/2}\pi^{2}}\int_{0}^{\infty}\frac{\modBesselK{1/3}@{t}}{\zeta^{2}+t^{2}}\diff{t}</math>]] || <code>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)</code> || <code>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}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.04337928599820519, -0.02597020526100885] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.04337928599820519, 0.02597020526100885] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
 
|-
 
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| [https://dlmf.nist.gov/9.12.E24 9.12.E24] || [[Item:Q2952|<math>\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}</math>]] || <code>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)</code> || <code>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}]</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/9.12.E24 9.12.E24] || [[Item:Q2952|<math>\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}</math>]] || <code>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)</code> || <code>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}]</code> || Failure || Failure || Skip || Error  
 
|-
 
|-
| [https://dlmf.nist.gov/9.13.E13 9.13.E13] || [[Item:Q2975|<math>\deriv[2]{w}{t} = \tfrac{1}{4}m^{2}t^{m-2}w</math>]] || <code>diff(w, [t$(2)])=(1)/(4)*(m)^(2)* (t)^(m - 2)* w</code> || <code>D[w, {t, 2}]=Divide[1,4]*(m)^(2)* (t)^(m - 2)* w</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.2500000000 <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 1}</code><br><code>-1.414213562-1.414213562*I <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 2}</code><br><code>-0.-8.999999996*I <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 3}</code><br><code>-0.+.2500000000*I <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), m = 1}</code><br><code>-1.414213562+1.414213562*I <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), m = 2}</code><br><code>-8.999999996-0.*I <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), m = 3}</code><br><code>.2500000000-0.*I <- {t = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2), m = 1}</code><br><code>1.414213562+1.414213562*I <- {t = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2), m = 2}</code><br><code>-0.+8.999999996*I <- {t = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2), m = 3}</code><br><code>-0.-.2500000000*I <- {t = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2), m = 1}</code><br><code>1.414213562-1.414213562*I <- {t = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2), m = 2}</code><br><code>8.999999996-0.*I <- {t = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2), m = 3}</code><br><code>-0.-.2500000000*I <- {t = 2^(1/2)-I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 1}</code><br><code>-1.414213562-1.414213562*I <- {t = 2^(1/2)-I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 2}</code><br><code>-8.999999996-0.*I <- {t = 2^(1/2)-I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 3}</code><br><code>-.2500000000 <- {t = 2^(1/2)-I*2^(1/2), w = 2^(1/2)-I*2^(1/2), m = 1}</code><br><code>-1.414213562+1.414213562*I <- {t = 2^(1/2)-I*2^(1/2), w = 2^(1/2)-I*2^(1/2), m = 2}</code><br><code>-0.+8.999999996*I <- {t = 2^(1/2)-I*2^(1/2), w = 2^(1/2)-I*2^(1/2), m = 3}</code><br><code>-0.+.2500000000*I <- {t = 2^(1/2)-I*2^(1/2), w = -2^(1/2)-I*2^(1/2), m = 1}</code><br><code>1.414213562+1.414213562*I <- {t = 2^(1/2)-I*2^(1/2), w = -2^(1/2)-I*2^(1/2), m = 2}</code><br><code>8.999999996-0.*I <- {t = 2^(1/2)-I*2^(1/2), w = -2^(1/2)-I*2^(1/2), m = 3}</code><br><code>.2500000000-0.*I <- {t = 2^(1/2)-I*2^(1/2), w = -2^(1/2)+I*2^(1/2), m = 1}</code><br><code>1.414213562-1.414213562*I <- {t = 2^(1/2)-I*2^(1/2), w = -2^(1/2)+I*2^(1/2), m = 2}</code><br><code>-0.-8.999999996*I <- {t = 2^(1/2)-I*2^(1/2), w = -2^(1/2)+I*2^(1/2), m = 3}</code><br><code>.2500000000-0.*I <- {t = -2^(1/2)-I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 1}</code><br><code>-1.414213562-1.414213562*I <- {t = -2^(1/2)-I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 2}</code><br><code>-0.+8.999999996*I <- {t = -2^(1/2)-I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 3}</code><br><code>-0.-.2500000000*I <- {t = -2^(1/2)-I*2^(1/2), w = 2^(1/2)-I*2^(1/2), m = 1}</code><br><code>-1.414213562+1.414213562*I <- {t = -2^(1/2)-I*2^(1/2), w = 2^(1/2)-I*2^(1/2), m = 2}</code><br><code>8.999999996-0.*I <- {t = -2^(1/2)-I*2^(1/2), w = 2^(1/2)-I*2^(1/2), m = 3}</code><br><code>-.2500000000 <- {t = -2^(1/2)-I*2^(1/2), w = -2^(1/2)-I*2^(1/2), m = 1}</code><br><code>1.414213562+1.414213562*I <- {t = -2^(1/2)-I*2^(1/2), w = -2^(1/2)-I*2^(1/2), m = 2}</code><br><code>-0.-8.999999996*I <- {t = -2^(1/2)-I*2^(1/2), w = -2^(1/2)-I*2^(1/2), m = 3}</code><br><code>-0.+.2500000000*I <- {t = -2^(1/2)-I*2^(1/2), w = -2^(1/2)+I*2^(1/2), m = 1}</code><br><code>1.414213562-1.414213562*I <- {t = -2^(1/2)-I*2^(1/2), w = -2^(1/2)+I*2^(1/2), m = 2}</code><br><code>-8.999999996-0.*I <- {t = -2^(1/2)-I*2^(1/2), w = -2^(1/2)+I*2^(1/2), m = 3}</code><br><code>-0.+.2500000000*I <- {t = -2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 1}</code><br><code>-1.414213562-1.414213562*I <- {t = -2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 2}</code><br><code>8.999999996-0.*I <- {t = -2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 3}</code><br><code>.2500000000-0.*I <- {t = -2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), m = 1}</code><br><code>-1.414213562+1.414213562*I <- {t = -2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), m = 2}</code><br><code>-0.-8.999999996*I <- {t = -2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), m = 3}</code><br><code>-0.-.2500000000*I <- {t = -2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2), m = 1}</code><br><code>1.414213562+1.414213562*I <- {t = -2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2), m = 2}</code><br><code>-8.999999996-0.*I <- {t = -2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2), m = 3}</code><br><code>-.2500000000 <- {t = -2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2), m = 1}</code><br><code>1.414213562-1.414213562*I <- {t = -2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2), m = 2}</code><br><code>-0.+8.999999996*I <- {t = -2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2), m = 3}</code><br></div></div> || Error  
+
| [https://dlmf.nist.gov/9.13.E13 9.13.E13] || [[Item:Q2975|<math>\deriv[2]{w}{t} = \tfrac{1}{4}m^{2}t^{m-2}w</math>]] || <code>diff(w, [t$(2)])=(1)/(4)*(m)^(2)* (t)^(m - 2)* w</code> || <code>D[w, {t, 2}]=Divide[1,4]*(m)^(2)* (t)^(m - 2)* w</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.2500000000 <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 1}</code><br><code>-1.414213562-1.414213562*I <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 2}</code><br><code>-0.-8.999999996*I <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 3}</code><br><code>-0.+.2500000000*I <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), m = 1}</code><br>... skip entries to safe data<br></div></div> || Error  
 
|-
 
|-
 
| [https://dlmf.nist.gov/9.13.E20 9.13.E20] || [[Item:Q2983|<math>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}}</math>]] || <code>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))</code> || <code>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)]</code> || Failure || Failure || Error || Error  
 
| [https://dlmf.nist.gov/9.13.E20 9.13.E20] || [[Item:Q2983|<math>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}}</math>]] || <code>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))</code> || <code>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)]</code> || Failure || Failure || Error || Error  

Latest revision as of 12:53, 19 January 2020

DLMF Formula Maple Mathematica Symbolic
Maple
Symbolic
Mathematica
Numeric
Maple
Numeric
Mathematica
9.2.E2 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 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 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 subs( temp=0, diff( AiryAi(temp), temp$(1) ) )= -(1)/((3)^(1/ 3)* GAMMA((1)/(3))) (D[AiryAi[temp], {temp, 1}]/.temp-> 0)= -Divide[1,(3)^(1/ 3)* Gamma[Divide[1,3]]] Successful Successful - -
9.2.E5 AiryBi(0)=(1)/((3)^(1/ 6)* GAMMA((2)/(3))) AiryBi[0]=Divide[1,(3)^(1/ 6)* Gamma[Divide[2,3]]] Successful Successful - -
9.2.E6 subs( temp=0, diff( AiryBi(temp), temp$(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 (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 (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 (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 (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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 (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 (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 (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 (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 (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 (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 subs( temp=z, diff( AiryAi(temp), temp$(1) ) )= - (Pi)^(- 1)*(z/sqrt(3))* BesselK(+ 2/ 3, (2)/(3)*(z)^((3)/(2))) (D[AiryAi[temp], {temp, 1}]/.temp-> z)= - (Pi)^(- 1)*(z/Sqrt[3])* BesselK[+ 2/ 3, Divide[2,3]*(z)^(Divide[3,2])] Failure Failure
Fail
-.7883076520+3.485863958*I <- {z = -2^(1/2)-I*2^(1/2)}
-.7883076520-3.485863958*I <- {z = -2^(1/2)+I*2^(1/2)}
Fail
Complex[-0.7883076520663912, 3.485863960601928] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.7883076520663912, -3.485863960601928] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E3 subs( temp=z, diff( AiryAi(temp), temp$(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 - (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 - (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 (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 (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 (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 (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 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 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 (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 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 (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 (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 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 (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 (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 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 (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 (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 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 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 (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 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