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| | <div style="-moz-column-count:2; column-count:2;"> |
| |- | | ; Notation : [[9.1|9.1 Special Notation]]<br> |
| ! DLMF !! Formula !! Constraints !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica
| | ; Airy Functions : [[9.2|9.2 Differential Equation]]<br>[[9.3|9.3 Graphics]]<br>[[9.4|9.4 Maclaurin Series]]<br>[[9.5|9.5 Integral Representations]]<br>[[9.6|9.6 Relations to Other Functions]]<br>[[9.7|9.7 Asymptotic Expansions]]<br>[[9.8|9.8 Modulus and Phase]]<br>[[9.9|9.9 Zeros]]<br>[[9.10|9.10 Integrals]]<br>[[9.11|9.11 Products]]<br> |
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| | ; Related Functions : [[9.12|9.12 Scorer Functions]]<br>[[9.13|9.13 Generalized Airy Functions]]<br>[[9.14|9.14 Incomplete Airy Functions]]<br> |
| | [https://dlmf.nist.gov/9.2.E2 9.2.E2] || [[Item:Q2754|<math>w = \AiryAi@{z},\;\AiryBi@{z},\;\AiryAi@{ze^{- 2\pi\iunit/3}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>w = AiryAi(z); AiryBi(z), AiryAi(z*exp(- 2*Pi*I/3))</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == AiryAi[z]
| | ; Applications : [[9.15|9.15 Mathematical Applications]]<br>[[9.16|9.16 Physical Applications]]<br> |
| AiryBi[z], AiryAi[z*Exp[- 2*Pi*I/3]]</syntaxhighlight> || Failure || Failure || Error || Error
| | ; Computation : [[9.17|9.17 Methods of Computation]]<br>[[9.18|9.18 Tables]]<br>[[9.19|9.19 Approximations]]<br>[[9.20|9.20 Software]]<br> |
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| | </div> |
| | [https://dlmf.nist.gov/9.2.E2 9.2.E2] || [[Item:Q2754|<math>w = \AiryAi@{z},\;\AiryBi@{z},\;\AiryAi@{ze^{+ 2\pi\iunit/3}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>w = AiryAi(z); AiryBi(z), AiryAi(z*exp(+ 2*Pi*I/3))</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == AiryAi[z]
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| AiryBi[z], AiryAi[z*Exp[+ 2*Pi*I/3]]</syntaxhighlight> || Failure || Failure || Error || Error
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| | [https://dlmf.nist.gov/9.2.E3 9.2.E3] || [[Item:Q2755|<math>\AiryAi@{0} = \frac{1}{3^{2/3}\EulerGamma@{\tfrac{2}{3}}}</math>]] || <math>\realpart@@{\tfrac{2}{3}} > 0</math> || <syntaxhighlight lang=mathematica>AiryAi(0) = (1)/((3)^(2/3)* GAMMA((2)/(3)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryAi[0] == Divide[1,(3)^(2/3)* Gamma[Divide[2,3]]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.2.E3 9.2.E3] || [[Item:Q2755|<math>\frac{1}{3^{2/3}\EulerGamma@{\tfrac{2}{3}}} = 0.35502\;80538\ldots</math>]] || <math>\realpart@@{\tfrac{2}{3}} > 0</math> || <syntaxhighlight lang=mathematica>(1)/((3)^(2/3)* GAMMA((2)/(3))) = 0.3550280538</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,(3)^(2/3)* Gamma[Divide[2,3]]] == 0.3550280538</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.2.E4 9.2.E4] || [[Item:Q2756|<math>\AiryAi'@{0} = -\frac{1}{3^{1/3}\EulerGamma@{\tfrac{1}{3}}}</math>]] || <math>\realpart@@{\tfrac{1}{3}} > 0</math> || <syntaxhighlight lang=mathematica>subs( temp=0, diff( AiryAi(temp), temp$(1) ) ) = -(1)/((3)^(1/3)* GAMMA((1)/(3)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[AiryAi[temp], {temp, 1}]/.temp-> 0) == -Divide[1,(3)^(1/3)* Gamma[Divide[1,3]]]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.2.E4 9.2.E4] || [[Item:Q2756|<math>-\frac{1}{3^{1/3}\EulerGamma@{\tfrac{1}{3}}} = -0.25881\;94037\ldots</math>]] || <math>\realpart@@{\tfrac{1}{3}} > 0</math> || <syntaxhighlight lang=mathematica>-(1)/((3)^(1/3)* GAMMA((1)/(3))) = - 0.2588194037</syntaxhighlight> || <syntaxhighlight lang=mathematica>-Divide[1,(3)^(1/3)* Gamma[Divide[1,3]]] == - 0.2588194037</syntaxhighlight> || Failure || Failure || Successful [Tested: 0] || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.2.E5 9.2.E5] || [[Item:Q2757|<math>\AiryBi@{0} = \frac{1}{3^{1/6}\EulerGamma@{\tfrac{2}{3}}}</math>]] || <math>\realpart@@{\tfrac{2}{3}} > 0</math> || <syntaxhighlight lang=mathematica>AiryBi(0) = (1)/((3)^(1/6)* GAMMA((2)/(3)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryBi[0] == Divide[1,(3)^(1/6)* Gamma[Divide[2,3]]]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.2.E5 9.2.E5] || [[Item:Q2757|<math>\frac{1}{3^{1/6}\EulerGamma@{\tfrac{2}{3}}} = 0.61492\;66274\ldots</math>]] || <math>\realpart@@{\tfrac{2}{3}} > 0</math> || <syntaxhighlight lang=mathematica>(1)/((3)^(1/6)* GAMMA((2)/(3))) = 0.6149266274</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,(3)^(1/6)* Gamma[Divide[2,3]]] == 0.6149266274</syntaxhighlight> || Failure || Failure || Successful [Tested: 0] || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.2.E6 9.2.E6] || [[Item:Q2758|<math>\AiryBi'@{0} = \frac{3^{1/6}}{\EulerGamma@{\tfrac{1}{3}}}</math>]] || <math>\realpart@@{\tfrac{1}{3}} > 0</math> || <syntaxhighlight lang=mathematica>subs( temp=0, diff( AiryBi(temp), temp$(1) ) ) = ((3)^(1/6))/(GAMMA((1)/(3)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[AiryBi[temp], {temp, 1}]/.temp-> 0) == Divide[(3)^(1/6),Gamma[Divide[1,3]]]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.2.E6 9.2.E6] || [[Item:Q2758|<math>\frac{3^{1/6}}{\EulerGamma@{\tfrac{1}{3}}} = 0.44828\;83573\ldots</math>]] || <math>\realpart@@{\tfrac{1}{3}} > 0</math> || <syntaxhighlight lang=mathematica>((3)^(1/6))/(GAMMA((1)/(3))) = 0.4482883573</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(3)^(1/6),Gamma[Divide[1,3]]] == 0.4482883573</syntaxhighlight> || Failure || Failure || Successful [Tested: 0] || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.2.E7 9.2.E7] || [[Item:Q2759|<math>\Wronskian@{\AiryAi@{z},\AiryBi@{z}} = \frac{1}{\pi}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(AiryAi(z))*diff(AiryBi(z), z)-diff(AiryAi(z), z)*(AiryBi(z)) = (1)/(Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Wronskian[{AiryAi[z], AiryBi[z]}, z] == Divide[1,Pi]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.2.E8 9.2.E8] || [[Item:Q2760|<math>\Wronskian@{\AiryAi@{z},\AiryAi@{ze^{- 2\pi i/3}}} = \frac{e^{+\pi i/6}}{2\pi}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Wronskian[{AiryAi[z], AiryAi[z*Exp[- 2*Pi*I/3]]}, z] == Divide[Exp[+ Pi*I/6],2*Pi]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.2.E8 9.2.E8] || [[Item:Q2760|<math>\Wronskian@{\AiryAi@{z},\AiryAi@{ze^{+ 2\pi i/3}}} = \frac{e^{-\pi i/6}}{2\pi}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Wronskian[{AiryAi[z], AiryAi[z*Exp[+ 2*Pi*I/3]]}, z] == Divide[Exp[- Pi*I/6],2*Pi]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.2.E9 9.2.E9] || [[Item:Q2761|<math>\Wronskian@{\AiryAi@{ze^{-2\pi i/3}},\AiryAi@{ze^{2\pi i/3}}} = \frac{1}{2\pi i}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Wronskian[{AiryAi[z*Exp[- 2*Pi*I/3]], AiryAi[z*Exp[2*Pi*I/3]]}, z] == Divide[1,2*Pi*I]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.2.E10 9.2.E10] || [[Item:Q2762|<math>\AiryBi@{z} = e^{-\pi i/6}\AiryAi@{ze^{-2\pi i/3}}+e^{\pi i/6}\AiryAi@{ze^{2\pi i/3}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryBi(z) = exp(- Pi*I/6)*AiryAi(z*exp(- 2*Pi*I/3))+ exp(Pi*I/6)*AiryAi(z*exp(2*Pi*I/3))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryBi[z] == Exp[- Pi*I/6]*AiryAi[z*Exp[- 2*Pi*I/3]]+ Exp[Pi*I/6]*AiryAi[z*Exp[2*Pi*I/3]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.2.E11 9.2.E11] || [[Item:Q2763|<math>\AiryAi@{ze^{- 2\pi i/3}} = \tfrac{1}{2}e^{-\pi i/3}\left(\AiryAi@{z}+ i\AiryBi@{z}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryAi(z*exp(- 2*Pi*I/3)) = (1)/(2)*exp(- Pi*I/3)*(AiryAi(z)+ I*AiryBi(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryAi[z*Exp[- 2*Pi*I/3]] == Divide[1,2]*Exp[- Pi*I/3]*(AiryAi[z]+ I*AiryBi[z])</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.2.E11 9.2.E11] || [[Item:Q2763|<math>\AiryAi@{ze^{+ 2\pi i/3}} = \tfrac{1}{2}e^{+\pi i/3}\left(\AiryAi@{z}- i\AiryBi@{z}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryAi(z*exp(+ 2*Pi*I/3)) = (1)/(2)*exp(+ Pi*I/3)*(AiryAi(z)- I*AiryBi(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryAi[z*Exp[+ 2*Pi*I/3]] == Divide[1,2]*Exp[+ Pi*I/3]*(AiryAi[z]- I*AiryBi[z])</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.2.E12 9.2.E12] || [[Item:Q2764|<math>\AiryAi@{z}+e^{-2\pi i/3}\AiryAi@{ze^{-2\pi i/3}}+e^{2\pi i/3}\AiryAi@{ze^{2\pi i/3}} = 0</math>]] || <math></math> || <syntaxhighlight lang=mathematica>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</syntaxhighlight> || <syntaxhighlight lang=mathematica>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</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.2.E13 9.2.E13] || [[Item:Q2765|<math>\AiryBi@{z}+e^{-2\pi i/3}\AiryBi@{ze^{-2\pi i/3}}+e^{2\pi i/3}\AiryBi@{ze^{2\pi i/3}} = 0</math>]] || <math></math> || <syntaxhighlight lang=mathematica>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</syntaxhighlight> || <syntaxhighlight lang=mathematica>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</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.2.E14 9.2.E14] || [[Item:Q2766|<math>\AiryAi@{-z} = e^{\pi i/3}\AiryAi@{ze^{\pi i/3}}+e^{-\pi i/3}\AiryAi@{ze^{-\pi i/3}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryAi(- z) = exp(Pi*I/3)*AiryAi(z*exp(Pi*I/3))+ exp(- Pi*I/3)*AiryAi(z*exp(- Pi*I/3))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryAi[- z] == Exp[Pi*I/3]*AiryAi[z*Exp[Pi*I/3]]+ Exp[- Pi*I/3]*AiryAi[z*Exp[- Pi*I/3]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryBi(- z) = exp(- Pi*I/6)*AiryAi(z*exp(Pi*I/3))+ exp(Pi*I/6)*AiryAi(z*exp(- Pi*I/3))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryBi[- z] == Exp[- Pi*I/6]*AiryAi[z*Exp[Pi*I/3]]+ Exp[Pi*I/6]*AiryAi[z*Exp[- Pi*I/3]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryAi(x) = (1)/(Pi)*int(cos((1)/(3)*(t)^(3)+ x*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryAi[x] == Divide[1,Pi]*Integrate[Cos[Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
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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>]] || <math>x > 0</math> || <syntaxhighlight lang=mathematica>AiryAi(- x) = ((x)^((1)/(2)))/(Pi)*int(cos((x)^((3)/(2))*((1)/(3)*(t)^(3)+ (t)^(2)-(2)/(3))), t = - 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryBi[x] == Divide[1,Pi]*Integrate[Exp[-Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}, GenerateConditions->None]+Divide[1,Pi]*Integrate[Sin[Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.510759173-.1408206709*I
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| Test Values: {x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2865429290-.9608783696e-1*I
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| Test Values: {x = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 3]
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1401376924-.8868274596e-1*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5566528573-.2432725641*I
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| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.14013769245288224, -0.08868274597809751], Times[Complex[0.0, 0.15915494309189535], NIntegrate[Power[E, Plus[Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], t], Times[Rational[1, 3], Power[t, 3]]]]
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| Test Values: {t, DirectedInfinity[Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], DirectedInfinity[Power[E, Times[Complex[0, Rational[1, 3]], Pi]]]}]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.5566528572571797, -0.24327256400505012], Times[Complex[0.0, 0.15915494309189535], NIntegrate[Power[E, Plus[Times[-1, Power[E, Times[Complex[0, Rational[2, 3]], Pi]], t], Times[Rational[1, 3], Power[t, 3]]]]
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| Test Values: {t, DirectedInfinity[Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], DirectedInfinity[Power[E, Times[Complex[0, Rational[1, 3]], Pi]]]}]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br</div></div>
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryBi[z] == Divide[1,2*Pi]*Integrate[Exp[Divide[1,3]*(t)^(3)- z*t], {t, - Infinity, Infinity*Exp[Pi*I/3]}, GenerateConditions->None]+Divide[1,2*Pi]*Integrate[Exp[Divide[1,3]*(t)^(3)- z*t], {t, - Infinity, Infinity*Exp[- Pi*I/3]}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Error || Skipped - Because timed out
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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>]] || <math>|\phase@@{z}| < \tfrac{1}{6}\cpi</math> || <syntaxhighlight lang=mathematica>AiryAi(z) = (sqrt(3))/(2*Pi)*int(exp(-((t)^(3))/(3)-((z)^(3))/(3*(t)^(3))), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryAi[z] == Divide[Sqrt[3],2*Pi]*Integrate[Exp[-Divide[(t)^(3),3]-Divide[(z)^(3),3*(t)^(3)]], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
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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>]] || <math>|\phase@@{z}| < \pi</math> || <syntaxhighlight lang=mathematica>AiryAi(z) = (exp(-(2)/(3)*(z)^((3)/(2))))/(Pi)*int(exp(- (z)^((1)/(2))* (t)^(2))*cos((1)/(3)*(t)^(3)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2560433475+.3687851240*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.0282029471418963, 0.1796919597060948]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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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>]] || <math>|\phase@@{z}| < \frac{2}{3}\pi, \realpart@@{\frac{5}{6}} > 0</math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [5 / 5]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5281740434e-1-.3342421534e-1*I
| |
| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .674352291e-1+.776049915e-1*I
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| Test Values: {z = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [5 / 5]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0528174043849943, -0.03342421567182417]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.06743522883170047, 0.07760499149873934]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</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>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryAi(z) = (Pi)^(- 1)*sqrt(z/3)*BesselK(+ 1/3, (2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryAi[z] == (Pi)^(- 1)*Sqrt[z/3]*BesselK[+ 1/3, Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.028202947+.1796919596*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.0282029471418963, 0.1796919597060948]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><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>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryAi(z) = (Pi)^(- 1)*sqrt(z/3)*BesselK(- 1/3, (2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryAi[z] == (Pi)^(- 1)*Sqrt[z/3]*BesselK[- 1/3, Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.028202947+.1796919596*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.0282029471418963, 0.1796919597060948]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><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>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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])])</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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])])</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
| |
| |-
| |
| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.045659506-.6037117977*I
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| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.028202948-.1796919595*I
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| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.045659506357919, -0.6037117974764359]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.0282029471418963, -0.1796919597060947]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| |-
| |
| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 7]
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| |-
| |
| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.045659507+.6037117981*I
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| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4467028535+.6697146486*I
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| Test Values: {z = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.0456595063579188, 0.6037117974764359]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.4467028530850735, 0.6697146479323786]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| |-
| |
| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 7]
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| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>diff( AiryAi(z), z$(1) ) = - (Pi)^(- 1)*(z/(sqrt(3)))*BesselK(+ 2/3, (2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[AiryAi[z], {z, 1}] == - (Pi)^(- 1)*(z/(Sqrt[3]))*BesselK[+ 2/3, Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2876791930+.6573919010*I
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| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.2876791932746734, 0.657391901009072]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| |-
| |
| | [https://dlmf.nist.gov/9.6.E3 9.6.E3] || [[Item:Q2783|<math>\AiryAi'@{z} = -\pi^{-1}(z/\sqrt{3})\modBesselK{- 2/3}@{\zeta}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff( AiryAi(z), z$(1) ) = - (Pi)^(- 1)*(z/(sqrt(3)))*BesselK(- 2/3, (2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[AiryAi[z], {z, 1}] == - (Pi)^(- 1)*(z/(Sqrt[3]))*BesselK[- 2/3, Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2876791930+.6573919010*I
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| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.2876791932746734, 0.657391901009072]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>- (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))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>- (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])])</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
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| |-
| |
| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>- (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))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>- (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])])</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
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| |-
| |
| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.8075132061-.4662179670*I
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| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2876791931-.6573919012*I
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| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.8075132057195985, -0.4662179666963879]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.2876791932746735, -0.6573919010090721]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><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{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>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 7]
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8075132066+.4662179669*I
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| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2641265961-.1348949430*I
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| Test Values: {z = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8075132057195987, 0.46621796669638804]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.26412659586991316, -0.13489494274589095]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</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>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 7]
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryBi(z) = sqrt(z/3)*(BesselI(1/3, (2)/(3)*(z)^((3)/(2)))+ BesselI(- 1/3, (2)/(3)*(z)^((3)/(2))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2310642860+.4406110717*I
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| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.23106428610863416, 0.44061107136250777]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><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>]] || <math></math> || <syntaxhighlight lang=mathematica>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)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.185673976+.6468773360e-1*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.199319247+.6472196920e-1*I
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| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.1856739752313228, 0.06468773371996589]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.1993192456185722, 0.06472196909084393]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>(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)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]])</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
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| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>diff( AiryBi(z), z$(1) ) = (z/(sqrt(3)))*(BesselI(2/3, (2)/(3)*(z)^((3)/(2)))+ BesselI(- 2/3, (2)/(3)*(z)^((3)/(2))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[AiryBi[z], {z, 1}] == (z/(Sqrt[3]))*(BesselI[2/3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselI[- 2/3, Divide[2,3]*(z)^(Divide[3,2])])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5692656477-.750312059e-1*I
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| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.5692656479003549, -0.07503120598537287]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>(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)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7341782379+.1916601474*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .6988938865-.1407017700*I
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| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.7341782376555157, 0.19166014735752115]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.6988938863252578, -0.14070176990144198]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| |-
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>(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)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]])</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
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| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryAi(- z) = (sqrt(z)/3)*(BesselJ(1/3, (2)/(3)*(z)^((3)/(2)))+ BesselJ(- 1/3, (2)/(3)*(z)^((3)/(2))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .309647027e-1+.3571238073*I
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| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.03096470287449324, 0.3571238071948327]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| | [https://dlmf.nist.gov/9.6.E6 9.6.E6] || [[Item:Q2786|<math>(\sqrt{z}/3)\left(\BesselJ{1/3}@{\zeta}+\BesselJ{-1/3}@{\zeta}\right) = \tfrac{1}{2}\sqrt{z/3}\left(e^{\pi i/6}\HankelH{1}{1/3}@{\zeta}+e^{-\pi i/6}\HankelH{2}{1/3}@{\zeta}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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])])</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.6.E6 9.6.E6] || [[Item:Q2786|<math>\tfrac{1}{2}\sqrt{z/3}\left(e^{\pi i/6}\HankelH{1}{1/3}@{\zeta}+e^{-\pi i/6}\HankelH{2}{1/3}@{\zeta}\right) = \tfrac{1}{2}\sqrt{z/3}\left(e^{-\pi i/6}\HankelH{1}{-1/3}@{\zeta}+e^{\pi i/6}\HankelH{2}{-1/3}@{\zeta}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])])</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.6.E7 9.6.E7] || [[Item:Q2787|<math>\AiryAi'@{-z} = (z/3)\left(\BesselJ{2/3}@{\zeta}-\BesselJ{-2/3}@{\zeta}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>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))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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])])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7438814497-.1824830770*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4379687237+.3495995698*I
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| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.7438814497662649, -0.18248307701953514]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.4379687237504881, 0.3495995697137311]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/9.6.E7 9.6.E7] || [[Item:Q2787|<math>(z/3)\left(\BesselJ{2/3}@{\zeta}-\BesselJ{-2/3}@{\zeta}\right) = \tfrac{1}{2}(z/\sqrt{3})\left(e^{-\pi i/6}\HankelH{1}{2/3}@{\zeta}+e^{\pi i/6}\HankelH{2}{2/3}@{\zeta}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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])])</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.6.E7 9.6.E7] || [[Item:Q2787|<math>\tfrac{1}{2}(z/\sqrt{3})\left(e^{-\pi i/6}\HankelH{1}{2/3}@{\zeta}+e^{\pi i/6}\HankelH{2}{2/3}@{\zeta}\right) = \tfrac{1}{2}(z/\sqrt{3})\left(e^{-5\pi i/6}\HankelH{1}{-2/3}@{\zeta}+e^{5\pi i/6}\HankelH{2}{-2/3}@{\zeta}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])])</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
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| |-
| |
| | [https://dlmf.nist.gov/9.6.E8 9.6.E8] || [[Item:Q2788|<math>\AiryBi@{-z} = \sqrt{z/3}\left(\BesselJ{-1/3}@{\zeta}-\BesselJ{1/3}@{\zeta}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryBi(- z) = sqrt(z/3)*(BesselJ(- 1/3, (2)/(3)*(z)^((3)/(2)))- BesselJ(1/3, (2)/(3)*(z)^((3)/(2))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.603467898+.7479320463*I
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| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.6034678974530832, 0.7479320460938138]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| |
| | [https://dlmf.nist.gov/9.6.E8 9.6.E8] || [[Item:Q2788|<math>\sqrt{z/3}\left(\BesselJ{-1/3}@{\zeta}-\BesselJ{1/3}@{\zeta}\right) = \tfrac{1}{2}\sqrt{z/3}\left(e^{2\pi i/3}\HankelH{1}{1/3}@{\zeta}+e^{-2\pi i/3}\HankelH{2}{1/3}@{\zeta}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>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))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])])</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 7]
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| |
| | [https://dlmf.nist.gov/9.6.E8 9.6.E8] || [[Item:Q2788|<math>\tfrac{1}{2}\sqrt{z/3}\left(e^{2\pi i/3}\HankelH{1}{1/3}@{\zeta}+e^{-2\pi i/3}\HankelH{2}{1/3}@{\zeta}\right) = \tfrac{1}{2}\sqrt{z/3}\left(e^{\pi i/3}\HankelH{1}{-1/3}@{\zeta}+e^{-\pi i/3}\HankelH{2}{-1/3}@{\zeta}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])])</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
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| |
| | [https://dlmf.nist.gov/9.6.E9 9.6.E9] || [[Item:Q2789|<math>\AiryBi'@{-z} = (z/\sqrt{3})\left(\BesselJ{-2/3}@{\zeta}+\BesselJ{2/3}@{\zeta}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>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))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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])])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4079506518-.4001199315*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5604204721-.1077527266*I
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| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.4079506515473492, -0.40011993153434466]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.5604204722153456, -0.10775272665850918]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| |
| | [https://dlmf.nist.gov/9.6.E9 9.6.E9] || [[Item:Q2789|<math>(z/\sqrt{3})\left(\BesselJ{-2/3}@{\zeta}+\BesselJ{2/3}@{\zeta}\right) = \tfrac{1}{2}(z/\sqrt{3})\left(e^{\pi i/3}\HankelH{1}{2/3}@{\zeta}+e^{-\pi i/3}\HankelH{2}{2/3}@{\zeta}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(z/(sqrt(3)))*(BesselJ(- 2/3, (2)/(3)*(z)^((3)/(2)))+ BesselJ(2/3, (2)/(3)*(z)^((3)/(2)))) = (1)/(2)*(z/(sqrt(3)))*(exp(Pi*I/3)*HankelH1(2/3, (2)/(3)*(z)^((3)/(2)))+ exp(- Pi*I/3)*HankelH2(2/3, (2)/(3)*(z)^((3)/(2))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(z/(Sqrt[3]))*(BesselJ[- 2/3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselJ[2/3, Divide[2,3]*(z)^(Divide[3,2])]) == Divide[1,2]*(z/(Sqrt[3]))*(Exp[Pi*I/3]*HankelH1[2/3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- Pi*I/3]*HankelH2[2/3, Divide[2,3]*(z)^(Divide[3,2])])</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 7]
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| |
| | [https://dlmf.nist.gov/9.6.E9 9.6.E9] || [[Item:Q2789|<math>\tfrac{1}{2}(z/\sqrt{3})\left(e^{\pi i/3}\HankelH{1}{2/3}@{\zeta}+e^{-\pi i/3}\HankelH{2}{2/3}@{\zeta}\right) = \tfrac{1}{2}(z/\sqrt{3})\left(e^{-\pi i/3}\HankelH{1}{-2/3}@{\zeta}+e^{\pi i/3}\HankelH{2}{-2/3}@{\zeta}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(1)/(2)*(z/(sqrt(3)))*(exp(Pi*I/3)*HankelH1(2/3, (2)/(3)*(z)^((3)/(2)))+ exp(- Pi*I/3)*HankelH2(2/3, (2)/(3)*(z)^((3)/(2)))) = (1)/(2)*(z/(sqrt(3)))*(exp(- Pi*I/3)*HankelH1(- 2/3, (2)/(3)*(z)^((3)/(2)))+ exp(Pi*I/3)*HankelH2(- 2/3, (2)/(3)*(z)^((3)/(2))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,2]*(z/(Sqrt[3]))*(Exp[Pi*I/3]*HankelH1[2/3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- Pi*I/3]*HankelH2[2/3, Divide[2,3]*(z)^(Divide[3,2])]) == Divide[1,2]*(z/(Sqrt[3]))*(Exp[- Pi*I/3]*HankelH1[- 2/3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[Pi*I/3]*HankelH2[- 2/3, Divide[2,3]*(z)^(Divide[3,2])])</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
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| |
| | [https://dlmf.nist.gov/9.6.E11 9.6.E11] || [[Item:Q2791|<math>\BesselJ{+ 1/3}@{\zeta} = \tfrac{1}{2}\sqrt{3/z}\left(\sqrt{3}\AiryAi@{-z}-\AiryBi@{-z}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>BesselJ(+ 1/3, (2)/(3)*(z)^((3)/(2))) = (1)/(2)*sqrt(3/z)*(sqrt(3)*AiryAi(- z)- AiryBi(- z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselJ[+ 1/3, Divide[2,3]*(z)^(Divide[3,2])] == Divide[1,2]*Sqrt[3/z]*(Sqrt[3]*AiryAi[- z]- AiryBi[- z])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2391614268+1.325461347*I
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| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.23916142675433638, 1.3254613471266568]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| |-
| |
| | [https://dlmf.nist.gov/9.6.E11 9.6.E11] || [[Item:Q2791|<math>\BesselJ{- 1/3}@{\zeta} = \tfrac{1}{2}\sqrt{3/z}\left(\sqrt{3}\AiryAi@{-z}+\AiryBi@{-z}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>BesselJ(- 1/3, (2)/(3)*(z)^((3)/(2))) = (1)/(2)*sqrt(3/z)*(sqrt(3)*AiryAi(- z)+ AiryBi(- z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselJ[- 1/3, Divide[2,3]*(z)^(Divide[3,2])] == Divide[1,2]*Sqrt[3/z]*(Sqrt[3]*AiryAi[- z]+ AiryBi[- z])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7716611346-1.692481494*I
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| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.7716611344125851, -1.6924814940408082]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| |-
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| | [https://dlmf.nist.gov/9.6.E12 9.6.E12] || [[Item:Q2792|<math>\BesselJ{+ 2/3}@{\zeta} = \tfrac{1}{2}(\sqrt{3}/z)\left(+\sqrt{3}\AiryAi'@{-z}+\AiryBi'@{-z}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>BesselJ(+ 2/3, (2)/(3)*(z)^((3)/(2))) = (1)/(2)*(sqrt(3)/z)*(+sqrt(3)*subs( temp=- z, diff( AiryAi(temp), temp$(1) ) )+ subs( temp=- z, diff( AiryBi(temp), temp$(1) ) ))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselJ[+ 2/3, Divide[2,3]*(z)^(Divide[3,2])] == Divide[1,2]*(Sqrt[3]/z)*(+Sqrt[3]*(D[AiryAi[temp], {temp, 1}]/.temp-> - z)+ (D[AiryBi[temp], {temp, 1}]/.temp-> - z))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .4073114590+.8284435869*I
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| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.40731145887570114, 0.8284435866207246]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| |-
| |
| | [https://dlmf.nist.gov/9.6.E12 9.6.E12] || [[Item:Q2792|<math>\BesselJ{- 2/3}@{\zeta} = \tfrac{1}{2}(\sqrt{3}/z)\left(-\sqrt{3}\AiryAi'@{-z}+\AiryBi'@{-z}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>BesselJ(- 2/3, (2)/(3)*(z)^((3)/(2))) = (1)/(2)*(sqrt(3)/z)*(-sqrt(3)*subs( temp=- z, diff( AiryAi(temp), temp$(1) ) )+ subs( temp=- z, diff( AiryBi(temp), temp$(1) ) ))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselJ[- 2/3, Divide[2,3]*(z)^(Divide[3,2])] == Divide[1,2]*(Sqrt[3]/z)*(-Sqrt[3]*(D[AiryAi[temp], {temp, 1}]/.temp-> - z)+ (D[AiryBi[temp], {temp, 1}]/.temp-> - z))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.051066782-.9245173022*I
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| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.0510667819735242, -0.9245173024955249]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| | [https://dlmf.nist.gov/9.6.E13 9.6.E13] || [[Item:Q2793|<math>\modBesselI{+ 1/3}@{\zeta} = \tfrac{1}{2}\sqrt{3/z}\left(-\sqrt{3}\AiryAi@{z}+\AiryBi@{z}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>BesselI(+ 1/3, (2)/(3)*(z)^((3)/(2))) = (1)/(2)*sqrt(3/z)*(-sqrt(3)*AiryAi(z)+ AiryBi(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[+ 1/3, Divide[2,3]*(z)^(Divide[3,2])] == Divide[1,2]*Sqrt[3/z]*(-Sqrt[3]*AiryAi[z]+ AiryBi[z])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .4556108026+1.267463912*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.4556108023887421, 1.2674639117231967]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| | [https://dlmf.nist.gov/9.6.E13 9.6.E13] || [[Item:Q2793|<math>\modBesselI{- 1/3}@{\zeta} = \tfrac{1}{2}\sqrt{3/z}\left(+\sqrt{3}\AiryAi@{z}+\AiryBi@{z}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>BesselI(- 1/3, (2)/(3)*(z)^((3)/(2))) = (1)/(2)*sqrt(3/z)*(+sqrt(3)*AiryAi(z)+ AiryBi(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[- 1/3, Divide[2,3]*(z)^(Divide[3,2])] == Divide[1,2]*Sqrt[3/z]*(+Sqrt[3]*AiryAi[z]+ AiryBi[z])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1779626013-1.851562537*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.1779626015059873, -1.8515625364806731]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| | [https://dlmf.nist.gov/9.6.E14 9.6.E14] || [[Item:Q2794|<math>\modBesselI{+ 2/3}@{\zeta} = \tfrac{1}{2}(\sqrt{3}/z)\left(+\sqrt{3}\AiryAi'@{z}+\AiryBi'@{z}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>BesselI(+ 2/3, (2)/(3)*(z)^((3)/(2))) = (1)/(2)*(sqrt(3)/z)*(+sqrt(3)*diff( AiryAi(z), z$(1) )+ diff( AiryBi(z), z$(1) ))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[+ 2/3, Divide[2,3]*(z)^(Divide[3,2])] == Divide[1,2]*(Sqrt[3]/z)*(+Sqrt[3]*D[AiryAi[z], {z, 1}]+ D[AiryBi[z], {z, 1}])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5137974625+.7669638641*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.5137974621779913, 0.7669638639492199]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| |-
| |
| | [https://dlmf.nist.gov/9.6.E14 9.6.E14] || [[Item:Q2794|<math>\modBesselI{- 2/3}@{\zeta} = \tfrac{1}{2}(\sqrt{3}/z)\left(-\sqrt{3}\AiryAi'@{z}+\AiryBi'@{z}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>BesselI(- 2/3, (2)/(3)*(z)^((3)/(2))) = (1)/(2)*(sqrt(3)/z)*(-sqrt(3)*diff( AiryAi(z), z$(1) )+ diff( AiryBi(z), z$(1) ))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[- 2/3, Divide[2,3]*(z)^(Divide[3,2])] == Divide[1,2]*(Sqrt[3]/z)*(-Sqrt[3]*D[AiryAi[z], {z, 1}]+ D[AiryBi[z], {z, 1}])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2751220789-1.372509185*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.2751220792126252, -1.372509185510794]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| |-
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| | [https://dlmf.nist.gov/9.6.E15 9.6.E15] || [[Item:Q2795|<math>\modBesselK{+ 1/3}@{\zeta} = \pi\sqrt{3/z}\AiryAi@{z}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>BesselK(+ 1/3, (2)/(3)*(z)^((3)/(2))) = Pi*sqrt(3/z)*AiryAi(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[+ 1/3, Divide[2,3]*(z)^(Divide[3,2])] == Pi*Sqrt[3/z]*AiryAi[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.5035981308-5.657288190*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.503598130241915, -5.657288188781889]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| |-
| |
| | [https://dlmf.nist.gov/9.6.E15 9.6.E15] || [[Item:Q2795|<math>\modBesselK{- 1/3}@{\zeta} = \pi\sqrt{3/z}\AiryAi@{z}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>BesselK(- 1/3, (2)/(3)*(z)^((3)/(2))) = Pi*sqrt(3/z)*AiryAi(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[- 1/3, Divide[2,3]*(z)^(Divide[3,2])] == Pi*Sqrt[3/z]*AiryAi[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.5035981308-5.657288190*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.503598130241915, -5.657288188781889]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/9.6.E16 9.6.E16] || [[Item:Q2796|<math>\modBesselK{+ 2/3}@{\zeta} = -\pi(\sqrt{3}/z)\AiryAi'@{z}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>BesselK(+ 2/3, (2)/(3)*(z)^((3)/(2))) = - Pi*(sqrt(3)/z)*diff( AiryAi(z), z$(1) )</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[+ 2/3, Divide[2,3]*(z)^(Divide[3,2])] == - Pi*(Sqrt[3]/z)*D[AiryAi[z], {z, 1}]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4329092589-3.880574857*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.43290925788093926, -3.8805748569068164]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| |-
| |
| | [https://dlmf.nist.gov/9.6.E16 9.6.E16] || [[Item:Q2796|<math>\modBesselK{- 2/3}@{\zeta} = -\pi(\sqrt{3}/z)\AiryAi'@{z}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>BesselK(- 2/3, (2)/(3)*(z)^((3)/(2))) = - Pi*(sqrt(3)/z)*diff( AiryAi(z), z$(1) )</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[- 2/3, Divide[2,3]*(z)^(Divide[3,2])] == - Pi*(Sqrt[3]/z)*D[AiryAi[z], {z, 1}]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4329092589-3.880574857*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.43290925788093926, -3.8805748569068164]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/9.6.E17 9.6.E17] || [[Item:Q2797|<math>\HankelH{1}{1/3}@{\zeta} = e^{-\pi i/3}\HankelH{1}{-1/3}@{\zeta}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>HankelH1(1/3, (2)/(3)*(z)^((3)/(2))) = exp(- Pi*I/3)*HankelH1(- 1/3, (2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>HankelH1[1/3, Divide[2,3]*(z)^(Divide[3,2])] == Exp[- Pi*I/3]*HankelH1[- 1/3, Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/9.6.E17 9.6.E17] || [[Item:Q2797|<math>e^{-\pi i/3}\HankelH{1}{-1/3}@{\zeta} = e^{-\pi i/6}\sqrt{3/z}\left(\AiryAi@{-z}-i\AiryBi@{-z}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>exp(- Pi*I/3)*HankelH1(- 1/3, (2)/(3)*(z)^((3)/(2))) = exp(- Pi*I/6)*sqrt(3/z)*(AiryAi(- z)- I*AiryBi(- z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[- Pi*I/3]*HankelH1[- 1/3, Divide[2,3]*(z)^(Divide[3,2])] == Exp[- Pi*I/6]*Sqrt[3/z]*(AiryAi[- z]- I*AiryBi[- z])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.480403332+.5725037338*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.480403331175524, 0.5725037338904919]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/9.6.E18 9.6.E18] || [[Item:Q2798|<math>\HankelH{1}{2/3}@{\zeta} = e^{-2\pi i/3}\HankelH{1}{-2/3}@{\zeta}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>HankelH1(2/3, (2)/(3)*(z)^((3)/(2))) = exp(- 2*Pi*I/3)*HankelH1(- 2/3, (2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>HankelH1[2/3, Divide[2,3]*(z)^(Divide[3,2])] == Exp[- 2*Pi*I/3]*HankelH1[- 2/3, Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/9.6.E18 9.6.E18] || [[Item:Q2798|<math>e^{-2\pi i/3}\HankelH{1}{-2/3}@{\zeta} = e^{\pi i/6}(\sqrt{3}/z)\left(\AiryAi'@{-z}-i\AiryBi'@{-z}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>exp(- 2*Pi*I/3)*HankelH1(- 2/3, (2)/(3)*(z)^((3)/(2))) = exp(Pi*I/6)*(sqrt(3)/z)*(subs( temp=- z, diff( AiryAi(temp), temp$(1) ) )- I*subs( temp=- z, diff( AiryBi(temp), temp$(1) ) ))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[- 2*Pi*I/3]*HankelH1[- 2/3, Divide[2,3]*(z)^(Divide[3,2])] == Exp[Pi*I/6]*(Sqrt[3]/z)*((D[AiryAi[temp], {temp, 1}]/.temp-> - z)- I*(D[AiryBi[temp], {temp, 1}]/.temp-> - z))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1819270397-.6203851736*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.18192704031292045, -0.6203851728225562]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/9.6.E19 9.6.E19] || [[Item:Q2799|<math>\HankelH{2}{1/3}@{\zeta} = e^{\pi i/3}\HankelH{2}{-1/3}@{\zeta}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>HankelH2(1/3, (2)/(3)*(z)^((3)/(2))) = exp(Pi*I/3)*HankelH2(- 1/3, (2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>HankelH2[1/3, Divide[2,3]*(z)^(Divide[3,2])] == Exp[Pi*I/3]*HankelH2[- 1/3, Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/9.6.E19 9.6.E19] || [[Item:Q2799|<math>e^{\pi i/3}\HankelH{2}{-1/3}@{\zeta} = e^{\pi i/6}\sqrt{3/z}\left(\AiryAi@{-z}+i\AiryBi@{-z}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>exp(Pi*I/3)*HankelH2(- 1/3, (2)/(3)*(z)^((3)/(2))) = exp(Pi*I/6)*sqrt(3/z)*(AiryAi(- z)+ I*AiryBi(- z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[Pi*I/3]*HankelH2[- 1/3, Divide[2,3]*(z)^(Divide[3,2])] == Exp[Pi*I/6]*Sqrt[3/z]*(AiryAi[- z]+ I*AiryBi[- z])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.958726185+2.078418961*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[2.958726184684197, 2.078418960362822]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/9.6.E20 9.6.E20] || [[Item:Q2800|<math>\HankelH{2}{2/3}@{\zeta} = e^{2\pi i/3}\HankelH{2}{-2/3}@{\zeta}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>HankelH2(2/3, (2)/(3)*(z)^((3)/(2))) = exp(2*Pi*I/3)*HankelH2(- 2/3, (2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>HankelH2[2/3, Divide[2,3]*(z)^(Divide[3,2])] == Exp[2*Pi*I/3]*HankelH2[- 2/3, Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/9.6.E20 9.6.E20] || [[Item:Q2800|<math>e^{2\pi i/3}\HankelH{2}{-2/3}@{\zeta} = e^{-\pi i/6}(\sqrt{3}/z)\left(\AiryAi'@{-z}+i\AiryBi'@{-z}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>exp(2*Pi*I/3)*HankelH2(- 2/3, (2)/(3)*(z)^((3)/(2))) = exp(- Pi*I/6)*(sqrt(3)/z)*(subs( temp=- z, diff( AiryAi(temp), temp$(1) ) )+ I*subs( temp=- z, diff( AiryBi(temp), temp$(1) ) ))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[2*Pi*I/3]*HankelH2[- 2/3, Divide[2,3]*(z)^(Divide[3,2])] == Exp[- Pi*I/6]*(Sqrt[3]/z)*((D[AiryAi[temp], {temp, 1}]/.temp-> - z)+ I*(D[AiryBi[temp], {temp, 1}]/.temp-> - z))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .9965499581+2.277272347*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.996549958064323, 2.277272346064005]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| |-
| |
| | [https://dlmf.nist.gov/9.6.E21 9.6.E21] || [[Item:Q2801|<math>\AiryAi@{z} = \tfrac{1}{2}\pi^{-1/2}z^{-1/4}\WhittakerconfhyperW{0}{1/3}@{2\zeta}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryAi(z) = (1)/(2)*(Pi)^(- 1/2)* (z)^(- 1/4)* WhittakerW(0, 1/3, 2*(2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryAi[z] == Divide[1,2]*(Pi)^(- 1/2)* (z)^(- 1/4)* WhittakerW[0, 1/3, 2*Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1468703571-.7702142875e-1*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.1468703571208359, -0.07702142870287806]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| |-
| |
| | [https://dlmf.nist.gov/9.6.E21 9.6.E21] || [[Item:Q2801|<math>\tfrac{1}{2}\pi^{-1/2}z^{-1/4}\WhittakerconfhyperW{0}{1/3}@{2\zeta} = 3^{-1/6}\pi^{-1/2}\zeta^{2/3}e^{-\zeta}\KummerconfhyperU@{\tfrac{5}{6}}{\tfrac{5}{3}}{2\zeta}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(1)/(2)*(Pi)^(- 1/2)* (z)^(- 1/4)* WhittakerW(0, 1/3, 2*(2)/(3)*(z)^((3)/(2))) = (3)^(- 1/6)* (Pi)^(- 1/2)*(2)/(3)*((z)^((3)/(2)))^(2/3)* exp(-(2)/(3)*(z)^((3)/(2)))*KummerU((5)/(6), (5)/(3), 2*(2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,2]*(Pi)^(- 1/2)* (z)^(- 1/4)* WhittakerW[0, 1/3, 2*Divide[2,3]*(z)^(Divide[3,2])] == (3)^(- 1/6)* (Pi)^(- 1/2)*Divide[2,3]*((z)^(Divide[3,2]))^(2/3)* Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricU[Divide[5,6], Divide[5,3], 2*Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .177161419e-1-.1121123152e-1*I
| |
| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .703717954e-1-.307544046e-1*I
| |
| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.017716141952820785, -0.011211231532459925]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.07037179551766398, -0.03075440448392741]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/9.6.E22 9.6.E22] || [[Item:Q2802|<math>\AiryAi'@{z} = -\tfrac{1}{2}\pi^{-1/2}z^{1/4}\WhittakerconfhyperW{0}{2/3}@{2\zeta}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff( AiryAi(z), z$(1) ) = -(1)/(2)*(Pi)^(- 1/2)* (z)^(1/4)* WhittakerW(0, 2/3, 2*(2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[AiryAi[z], {z, 1}] == -Divide[1,2]*(Pi)^(- 1/2)* (z)^(1/4)* WhittakerW[0, 2/3, 2*Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.250104019e-1-.1897552162*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.025010401995124304, -0.18975521596678477]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/9.6.E22 9.6.E22] || [[Item:Q2802|<math>-\tfrac{1}{2}\pi^{-1/2}z^{1/4}\WhittakerconfhyperW{0}{2/3}@{2\zeta} = -3^{1/6}\pi^{-1/2}\zeta^{4/3}e^{-\zeta}\KummerconfhyperU@{\tfrac{7}{6}}{\tfrac{7}{3}}{2\zeta}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>-(1)/(2)*(Pi)^(- 1/2)* (z)^(1/4)* WhittakerW(0, 2/3, 2*(2)/(3)*(z)^((3)/(2))) = - (3)^(1/6)* (Pi)^(- 1/2)*(2)/(3)*((z)^((3)/(2)))^(4/3)* exp(-(2)/(3)*(z)^((3)/(2)))*KummerU((7)/(6), (7)/(3), 2*(2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>-Divide[1,2]*(Pi)^(- 1/2)* (z)^(1/4)* WhittakerW[0, 2/3, 2*Divide[2,3]*(z)^(Divide[3,2])] == - (3)^(1/6)* (Pi)^(- 1/2)*Divide[2,3]*((z)^(Divide[3,2]))^(4/3)* Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricU[Divide[7,6], Divide[7,3], 2*Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .255909826e-1-.1059568228e-1*I
| |
| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .641870571e-1+.237615168e-1*I
| |
| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.025590982799820167, -0.01059568227344454]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.06418705631415383, 0.02376151710604532]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/9.6.E23 9.6.E23] || [[Item:Q2803|<math>\AiryBi@{z} = \frac{1}{2^{1/3}\EulerGamma@{\tfrac{2}{3}}}z^{-1/4}\WhittakerconfhyperM{0}{-1/3}@{2\zeta}+\frac{3}{2^{5/3}\EulerGamma@{\tfrac{1}{3}}}z^{-1/4}\WhittakerconfhyperM{0}{1/3}@{2\zeta}</math>]] || <math>\realpart@@{\tfrac{2}{3}} > 0, \realpart@@{\tfrac{1}{3}} > 0</math> || <syntaxhighlight lang=mathematica>AiryBi(z) = (1)/((2)^(1/3)* GAMMA((2)/(3)))*(z)^(- 1/4)* WhittakerM(0, - 1/3, 2*(2)/(3)*(z)^((3)/(2)))+(3)/((2)^(5/3)* GAMMA((1)/(3)))*(z)^(- 1/4)* WhittakerM(0, 1/3, 2*(2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryBi[z] == Divide[1,(2)^(1/3)* Gamma[Divide[2,3]]]*(z)^(- 1/4)* WhittakerM[0, - 1/3, 2*Divide[2,3]*(z)^(Divide[3,2])]+Divide[3,(2)^(5/3)* Gamma[Divide[1,3]]]*(z)^(- 1/4)* WhittakerM[0, 1/3, 2*Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1796919595-1.028202947*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.17969195970609464, -1.0282029471418963]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
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| |-
| |
| | [https://dlmf.nist.gov/9.6.E24 9.6.E24] || [[Item:Q2804|<math>\AiryBi'@{z} = \frac{2^{1/3}}{\EulerGamma@{\tfrac{1}{3}}}z^{1/4}\WhittakerconfhyperM{0}{-2/3}@{2\zeta}+\frac{3}{2^{10/3}\EulerGamma@{\tfrac{2}{3}}}z^{1/4}\WhittakerconfhyperM{0}{2/3}@{2\zeta}</math>]] || <math>\realpart@@{\tfrac{1}{3}} > 0, \realpart@@{\tfrac{2}{3}} > 0</math> || <syntaxhighlight lang=mathematica>diff( AiryBi(z), z$(1) ) = ((2)^(1/3))/(GAMMA((1)/(3)))*(z)^(1/4)* WhittakerM(0, - 2/3, 2*(2)/(3)*(z)^((3)/(2)))+(3)/((2)^(10/3)* GAMMA((2)/(3)))*(z)^(1/4)* WhittakerM(0, 2/3, 2*(2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[AiryBi[z], {z, 1}] == Divide[(2)^(1/3),Gamma[Divide[1,3]]]*(z)^(1/4)* WhittakerM[0, - 2/3, 2*Divide[2,3]*(z)^(Divide[3,2])]+Divide[3,(2)^(10/3)* Gamma[Divide[2,3]]]*(z)^(1/4)* WhittakerM[0, 2/3, 2*Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6573919012+.2876791929*I
| |
| Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6573919010090719, 0.2876791932746734]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/9.6.E25 9.6.E25] || [[Item:Q2805|<math>\AiryBi@{z} = \frac{1}{3^{1/6}\EulerGamma@{\tfrac{2}{3}}}e^{-\zeta}\genhyperF{1}{1}@{\tfrac{1}{6}}{\tfrac{1}{3}}{2\zeta}+\frac{3^{5/6}}{2^{2/3}\EulerGamma@{\tfrac{1}{3}}}\zeta^{2/3}e^{-\zeta}\genhyperF{1}{1}@{\tfrac{5}{6}}{\tfrac{5}{3}}{2\zeta}</math>]] || <math>\realpart@@{\tfrac{2}{3}} > 0, \realpart@@{\tfrac{1}{3}} > 0</math> || <syntaxhighlight lang=mathematica>AiryBi(z) = (1)/((3)^(1/6)* GAMMA((2)/(3)))*exp(-(2)/(3)*(z)^((3)/(2)))*hypergeom([(1)/(6)], [(1)/(3)], 2*(2)/(3)*(z)^((3)/(2)))+((3)^(5/6))/((2)^(2/3)* GAMMA((1)/(3)))*(2)/(3)*((z)^((3)/(2)))^(2/3)* exp(-(2)/(3)*(z)^((3)/(2)))*hypergeom([(5)/(6)], [(5)/(3)], 2*(2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryBi[z] == Divide[1,(3)^(1/6)* Gamma[Divide[2,3]]]*Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricPFQ[{Divide[1,6]}, {Divide[1,3]}, 2*Divide[2,3]*(z)^(Divide[3,2])]+Divide[(3)^(5/6),(2)^(2/3)* Gamma[Divide[1,3]]]*Divide[2,3]*((z)^(Divide[3,2]))^(2/3)* Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricPFQ[{Divide[5,6]}, {Divide[5,3]}, 2*Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .466216443e-1+.323688811e-1*I
| |
| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.307544045e-1+.532681913e-1*I
| |
| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.04662164404767005, 0.03236888089707873]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.030754404483927522, 0.05326819112268627]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/9.6.E26 9.6.E26] || [[Item:Q2806|<math>\AiryBi'@{z} = \frac{3^{1/6}}{\EulerGamma@{\tfrac{1}{3}}}e^{-\zeta}\genhyperF{1}{1}@{-\tfrac{1}{6}}{-\tfrac{1}{3}}{2\zeta}+\frac{3^{7/6}}{2^{7/3}\EulerGamma@{\tfrac{2}{3}}}\zeta^{4/3}e^{-\zeta}\genhyperF{1}{1}@{\tfrac{7}{6}}{\tfrac{7}{3}}{2\zeta}</math>]] || <math>\realpart@@{\tfrac{1}{3}} > 0, \realpart@@{\tfrac{2}{3}} > 0</math> || <syntaxhighlight lang=mathematica>diff( AiryBi(z), z$(1) ) = ((3)^(1/6))/(GAMMA((1)/(3)))*exp(-(2)/(3)*(z)^((3)/(2)))*hypergeom([-(1)/(6)], [-(1)/(3)], 2*(2)/(3)*(z)^((3)/(2)))+((3)^(7/6))/((2)^(7/3)* GAMMA((2)/(3)))*(2)/(3)*((z)^((3)/(2)))^(4/3)* exp(-(2)/(3)*(z)^((3)/(2)))*hypergeom([(7)/(6)], [(7)/(3)], 2*(2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[AiryBi[z], {z, 1}] == Divide[(3)^(1/6),Gamma[Divide[1,3]]]*Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricPFQ[{-Divide[1,6]}, {-Divide[1,3]}, 2*Divide[2,3]*(z)^(Divide[3,2])]+Divide[(3)^(7/6),(2)^(7/3)* Gamma[Divide[2,3]]]*Divide[2,3]*((z)^(Divide[3,2]))^(4/3)* Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricPFQ[{Divide[7,6]}, {Divide[7,3]}, 2*Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.196479231e-1-.399625288e-1*I
| |
| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .237615179e-1+.411561548e-1*I
| |
| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.01964792308482996, -0.03996252871199468]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.02376151710604532, 0.041156154892587504]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/9.7#Ex2 9.7#Ex2] || [[Item:Q2809|<math>v_{k} = \frac{6k+1}{1-6k}u_{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>v[k] = (6*k + 1)/(1 - 6*k)*u[k]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[v, k] == Divide[6*k + 1,1 - 6*k]*Subscript[u, k]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| |-
| |
| | [https://dlmf.nist.gov/9.7#Ex3 9.7#Ex3] || [[Item:Q2822|<math>\AiryAi@{x} \leq \frac{e^{-\xi}}{2\sqrt{\pi}x^{1/4}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryAi(x) <= (exp(- xi))/(2*sqrt(Pi)*(x)^(1/4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryAi[x] <= Divide[Exp[- \[Xi]],2*Sqrt[Pi]*(x)^(1/4)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7174949701e-1 <= .5687619445e-1
| |
| Test Values: {x = 1.5, xi = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .7174949701e-1 <= .3449715573e-1
| |
| Test Values: {x = 1.5, xi = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[0.07174949700810541, Complex[0.09409145494595897, -0.05140239611000222]]
| |
| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[0.07174949700810541, Complex[0.2722702697816324, -0.3201383097997893]]
| |
| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| |-
| |
| | [https://dlmf.nist.gov/9.7#Ex4 9.7#Ex4] || [[Item:Q2823|<math>|\AiryAi'@{x}| \leq \frac{x^{1/4}e^{-\xi}}{2\sqrt{\pi}}\left(1+\frac{7}{72\xi}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>abs(diff( AiryAi(x), x$(1) )) <= ((x)^(1/4)* exp(- xi))/(2*sqrt(Pi))*(1 +(7)/(72*xi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[D[AiryAi[x], {x, 1}]] <= Divide[(x)^(1/4)* Exp[- \[Xi]],2*Sqrt[Pi]]*(1 +Divide[7,72*\[Xi]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .9738201284e-1 <= .7417375145e-1
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| Test Values: {x = 1.5, xi = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .9738201284e-1 <= .4430404444e-1
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| Test Values: {x = 1.5, xi = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[0.0973820128423013, Complex[0.12188040935651077, -0.07385727120906739]]
| |
| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[0.0973820128423013, Complex[0.2842390979283623, -0.4011043708701865]]
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| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| |-
| |
| | [https://dlmf.nist.gov/9.7#Ex5 9.7#Ex5] || [[Item:Q2824|<math>\AiryBi@{x} \leq \frac{\expe^{\xi}}{\sqrt{\cpi}x^{1/4}}\left(1+\left(\chi(\tfrac{7}{6})+1\right)\frac{5}{72\xi}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryBi(x) <= (exp(xi))/(sqrt(Pi)*(x)^(1/4))*(1 +(chi((7)/(6))+ 1)*(5)/(72*xi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryBi[x] <= Divide[Exp[\[Xi]],Sqrt[Pi]*(x)^(1/4)]*(1 +(\[Chi][Divide[7,6]]+ 1)*Divide[5,72*\[Xi]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [72 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.878941504 <= .1177021246
| |
| Test Values: {chi = -1.5, x = 1.5, xi = -1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.878941504 <= .3414205364
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| Test Values: {chi = -1.5, x = 1.5, xi = -.5}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [264 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[1.8789415037478943, Complex[1.2339745412017042, 0.6261685922908564]]
| |
| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[1.8789415037478943, Complex[1.1007209136525415, 0.6652662717134934]]
| |
| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[χ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| |-
| |
| | [https://dlmf.nist.gov/9.7#Ex6 9.7#Ex6] || [[Item:Q2825|<math>\AiryBi'@{x} \leq \frac{x^{1/4}e^{\xi}}{\sqrt{\pi}}\left(1+\left(\frac{\cpi}{2}+1\right)\frac{7}{72\xi}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff( AiryBi(x), x$(1) ) <= ((x)^(1/4)* exp(xi))/(sqrt(Pi))*(1 +((Pi)/(2)+ 1)*(7)/(72*xi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[AiryBi[x], {x, 1}] <= Divide[(x)^(1/4)* Exp[\[Xi]],Sqrt[Pi]]*(1 +(Divide[Pi,2]+ 1)*Divide[7,72*\[Xi]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [12 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.886212255 <= .1161037548
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| Test Values: {x = 1.5, xi = -1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.886212255 <= .1893988815
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| Test Values: {x = 1.5, xi = -.5}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [24 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[1.8862122548481652, Complex[1.673615932813246, 0.7029160379352533]]
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| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[1.8862122548481652, Complex[0.2771293070670663, 0.19932445926872913]]
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| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| |-
| |
| | [https://dlmf.nist.gov/9.7.E18 9.7.E18] || [[Item:Q2827|<math>\AiryAi@{z} = \frac{e^{-\zeta}}{2\sqrt{\pi}z^{1/4}}\left(\sum_{k=0}^{n-1}(-1)^{k}\frac{u_{k}}{\zeta^{k}}+R_{n}(z)\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryAi(z) = (exp(-(2)/(3)*(z)^((3)/(2))))/(2*sqrt(Pi)*(z)^(1/4))*(sum((- 1)^(k)*(u[k])/((2)/(3)*((z)^((3)/(2)))^(k)), k = 0..n - 1)+ R[n](z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryAi[z] == Divide[Exp[-Divide[2,3]*(z)^(Divide[3,2])],2*Sqrt[Pi]*(z)^(1/4)]*(Sum[(- 1)^(k)*Divide[Subscript[u, k],Divide[2,3]*((z)^(Divide[3,2]))^(k)], {k, 0, n - 1}, GenerateConditions->None]+ Subscript[R, n][z])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2820623089-.1436891013*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I, R[n] = 1/2*3^(1/2)+1/2*I, u[k] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1105804716-.3445358858*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I, R[n] = 1/2*3^(1/2)+1/2*I, u[k] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
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| |-
| |
| | [https://dlmf.nist.gov/9.7.E19 9.7.E19] || [[Item:Q2828|<math>\AiryAi'@{z} = -\frac{z^{1/4}e^{-\zeta}}{2\sqrt{\pi}}\left(\sum_{k=0}^{n-1}(-1)^{k}\frac{v_{k}}{\zeta^{k}}+S_{n}(z)\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff( AiryAi(z), z$(1) ) = -((z)^(1/4)* exp(-(2)/(3)*(z)^((3)/(2))))/(2*sqrt(Pi))*(sum((- 1)^(k)*(v[k])/((2)/(3)*((z)^((3)/(2)))^(k)), k = 0..n - 1)+ S[n](z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[AiryAi[z], {z, 1}] == -Divide[(z)^(1/4)* Exp[-Divide[2,3]*(z)^(Divide[3,2])],2*Sqrt[Pi]]*(Sum[(- 1)^(k)*Divide[Subscript[v, k],Divide[2,3]*((z)^(Divide[3,2]))^(k)], {k, 0, n - 1}, GenerateConditions->None]+ Subscript[S, n][z])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2167391543+.2356234249*I
| |
| Test Values: {z = 1/2*3^(1/2)+1/2*I, S[n] = 1/2*3^(1/2)+1/2*I, v[k] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.8825541e-3+.3852437556*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I, S[n] = 1/2*3^(1/2)+1/2*I, v[k] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
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| |-
| |
| | [https://dlmf.nist.gov/9.7.E22 9.7.E22] || [[Item:Q2831|<math>\scterminant{p}@{z} = \frac{e^{z}}{2\pi}\EulerGamma@{p}\incGamma@{1-p}{z}</math>]] || <math>\realpart@@{p} > 0</math> || <syntaxhighlight lang=mathematica>(exp(z)/(2*Pi))*GAMMA(p)*GAMMA(1-p,z) = (exp(z))/(2*Pi)*GAMMA(p)*GAMMA(1 - p, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
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| |-
| |
| | [https://dlmf.nist.gov/9.8.E1 9.8.E1] || [[Item:Q2833|<math>\AiryAi@{x} = \AirymodM@{x}\sin@@{\Airyphasetheta@{x}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryAi(x) = sqrt(AiryAi(x)^2+AiryBi(x)^2)*sin(arctan(AiryAi(x)/AiryBi(x)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryAi[x] == Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*Sin[ArcTan[Divide[AiryAi[x], AiryBi[x]]]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
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| |-
| |
| | [https://dlmf.nist.gov/9.8.E2 9.8.E2] || [[Item:Q2834|<math>\AiryBi@{x} = \AirymodM@{x}\cos@@{\Airyphasetheta@{x}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryBi(x) = sqrt(AiryAi(x)^2+AiryBi(x)^2)*cos(arctan(AiryAi(x)/AiryBi(x)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryBi[x] == Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*Cos[ArcTan[Divide[AiryAi[x], AiryBi[x]]]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
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| |-
| |
| | [https://dlmf.nist.gov/9.8.E3 9.8.E3] || [[Item:Q2835|<math>\AirymodM@{x} = \sqrt{\AiryAi^{2}@{x}+\AiryBi^{2}@{x}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sqrt(AiryAi(x)^2+AiryBi(x)^2) = sqrt((AiryAi(x))^(2)+ (AiryBi(x))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sqrt[AiryAi[x]^2 + AiryBi[x]^2] == Sqrt[(AiryAi[x])^(2)+ (AiryBi[x])^(2)]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
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| |-
| |
| | [https://dlmf.nist.gov/9.8.E4 9.8.E4] || [[Item:Q2836|<math>\Airyphasetheta@{x} = \atan@{\AiryAi@{x}/\AiryBi@{x}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>arctan(AiryAi(x)/AiryBi(x)) = arctan(AiryAi(x)/AiryBi(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[Divide[AiryAi[x], AiryBi[x]]] == ArcTan[AiryAi[x]/AiryBi[x]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
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| |-
| |
| | [https://dlmf.nist.gov/9.8.E5 9.8.E5] || [[Item:Q2837|<math>\AiryAi'@{x} = \AirymodderivN@{x}\sin@@{\Airyphasederivphi@{x}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff( AiryAi(x), x$(1) ) = sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2)*sin(arctan(AiryAi(1, x)/AiryBi(1, x)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[AiryAi[x], {x, 1}] == Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2]*Sin[ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
| |
| |-
| |
| | [https://dlmf.nist.gov/9.8.E6 9.8.E6] || [[Item:Q2838|<math>\AiryBi'@{x} = \AirymodderivN@{x}\cos@@{\Airyphasederivphi@{x}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff( AiryBi(x), x$(1) ) = sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2)*cos(arctan(AiryAi(1, x)/AiryBi(1, x)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[AiryBi[x], {x, 1}] == Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2]*Cos[ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
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| |-
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| | [https://dlmf.nist.gov/9.8.E7 9.8.E7] || [[Item:Q2839|<math>\AirymodderivN@{x} = \sqrt{\AiryAi'^{2}@{x}+\AiryBi'^{2}@{x}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2) = sqrt((diff( AiryAi(x), x$(1) ))^(2)+ (diff( AiryBi(x), x$(1) ))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2] == Sqrt[(D[AiryAi[x], {x, 1}])^(2)+ (D[AiryBi[x], {x, 1}])^(2)]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
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| |-
| |
| | [https://dlmf.nist.gov/9.8.E8 9.8.E8] || [[Item:Q2840|<math>\Airyphasederivphi@{x} = \atan@{\AiryAi'@{x}/\AiryBi'@{x}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>arctan(AiryAi(1, x)/AiryBi(1, x)) = arctan(diff( AiryAi(x), x$(1) )/diff( AiryBi(x), x$(1) ))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]] == ArcTan[D[AiryAi[x], {x, 1}]/D[AiryBi[x], {x, 1}]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
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| |-
| |
| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 4.021808267-.8614613375e-2*I
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| Test Values: {x = 1.5, xi = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.972124824-.1350954874e-1*I
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| Test Values: {x = 1.5, xi = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[4.021808267868023, -0.008614613397096321]
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| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[3.972124824572757, -0.01350954875717339]
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| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| |-
| |
| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.579966574+.1365442595e-1*I
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| Test Values: {x = 1.5, xi = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.649043945+.8067203529e-2*I
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| Test Values: {x = 1.5, xi = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[2.579966572371216, 0.013654425864881942]
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| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[2.6490439435787625, 0.00806720349537901]
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| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| |-
| |
| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>arctan(AiryAi(x)/AiryBi(x)) = (2)/(3)*Pi + arctan(BesselY(1/3, xi)/BesselJ(1/3, xi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[Divide[AiryAi[x], AiryBi[x]]] == Divide[2,3]*Pi + ArcTan[BesselY[1/3, \[Xi]]/BesselJ[1/3, \[Xi]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.560189280-.5213615815*I
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| Test Values: {x = 1.5, xi = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.390111334-.9722564139*I
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| Test Values: {x = 1.5, xi = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.5601892780520927, -0.5213615814894055]
| |
| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.390111332221422, -0.9722564141048874]
| |
| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| |-
| |
| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>arctan(AiryAi(1, x)/AiryBi(1, x)) = (1)/(3)*Pi + arctan(BesselY(2/3, xi)/BesselJ(2/3, xi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]] == Divide[1,3]*Pi + ArcTan[BesselY[2/3, \[Xi]]/BesselJ[2/3, \[Xi]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2068569407-.4703554156*I
| |
| Test Values: {x = 1.5, xi = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.895355428-.7064271023*I
| |
| Test Values: {x = 1.5, xi = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.20685694111550512, -0.47035541563882277]
| |
| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.8953554288661256, -0.7064271020951838]
| |
| Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
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| |-
| |
| | [https://dlmf.nist.gov/9.8#Ex1 9.8#Ex1] || [[Item:Q2846|<math>\AirymodM^{2}@{x}\Airyphasetheta'@{x} = -\pi^{-1}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)* diff( arctan(AiryAi(x)/AiryBi(x)), x$(1) ) = - (Pi)^(- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)* D[ArcTan[Divide[AiryAi[x], AiryBi[x]]], {x, 1}] == - (Pi)^(- 1)</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
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| |-
| |
| | [https://dlmf.nist.gov/9.8#Ex2 9.8#Ex2] || [[Item:Q2847|<math>\AirymodderivN^{2}@{x}\Airyphasederivphi'@{x} = \pi^{-1}x</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2)* diff( arctan(AiryAi(1, x)/AiryBi(1, x)), x$(1) ) = (Pi)^(- 1)* x</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(2)* D[ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]], {x, 1}] == (Pi)^(- 1)* x</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
| |
| |-
| |
| | [https://dlmf.nist.gov/9.8#Ex3 9.8#Ex3] || [[Item:Q2848|<math>\AirymodderivN@{x}\AirymodderivN'@{x} = x\AirymodM@{x}\AirymodM'@{x}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2)*diff( sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2), x$(1) ) = x*sqrt(AiryAi(x)^2+AiryBi(x)^2)*diff( sqrt(AiryAi(x)^2+AiryBi(x)^2), x$(1) )</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2]*D[Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2], {x, 1}] == x*Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*D[Sqrt[AiryAi[x]^2 + AiryBi[x]^2], {x, 1}]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
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| |-
| |
| | [https://dlmf.nist.gov/9.8.E15 9.8.E15] || [[Item:Q2849|<math>\AirymodderivN^{2}@{x} = \AirymodM'^{2}@{x}+\AirymodM^{2}@{x}\Airyphasetheta'^{2}@{x}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2) = (diff( sqrt(AiryAi(x)^2+AiryBi(x)^2), x$(1) ))^(2)+ (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)* (diff( arctan(AiryAi(x)/AiryBi(x)), x$(1) ))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(2) == (D[Sqrt[AiryAi[x]^2 + AiryBi[x]^2], {x, 1}])^(2)+ (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)* (D[ArcTan[Divide[AiryAi[x], AiryBi[x]]], {x, 1}])^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
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| |-
| |
| | [https://dlmf.nist.gov/9.8.E15 9.8.E15] || [[Item:Q2849|<math>\AirymodM'^{2}@{x}+\AirymodM^{2}@{x}\Airyphasetheta'^{2}@{x} = \AirymodM'^{2}(x)+\pi^{-2}\AirymodM^{-2}@{x}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff( sqrt(AiryAi(x)^2+AiryBi(x)^2), x$(1) ))^(2)+ (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)* (diff( arctan(AiryAi(x)/AiryBi(x)), x$(1) ))^(2) = (subs( temp=(x), diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) ))^(2)+ (Pi)^(- 2)* (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(- 2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[Sqrt[AiryAi[x]^2 + AiryBi[x]^2], {x, 1}])^(2)+ (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)* (D[ArcTan[Divide[AiryAi[x], AiryBi[x]]], {x, 1}])^(2) == ((D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> (x)))^(2)+ (Pi)^(- 2)* (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(- 2)</syntaxhighlight> || Translation Error || Translation Error || - || -
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| |-
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| | [https://dlmf.nist.gov/9.8.E16 9.8.E16] || [[Item:Q2850|<math>x^{2}\AirymodM^{2}@{x} = \AirymodderivN'^{2}@{x}+\AirymodderivN^{2}@{x}\Airyphasederivphi'^{2}@{x}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(x)^(2)* (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2) = (diff( sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2), x$(1) ))^(2)+ (sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2)* (diff( arctan(AiryAi(1, x)/AiryBi(1, x)), x$(1) ))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(x)^(2)* (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2) == (D[Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2], {x, 1}])^(2)+ (Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(2)* (D[ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]], {x, 1}])^(2)</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 3]
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| |-
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| | [https://dlmf.nist.gov/9.8.E16 9.8.E16] || [[Item:Q2850|<math>\AirymodderivN'^{2}@{x}+\AirymodderivN^{2}@{x}\Airyphasederivphi'^{2}@{x} = \AirymodderivN'^{2}@{x}+\pi^{-2}x^{2}\AirymodderivN^{-2}@{x}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff( sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2), x$(1) ))^(2)+ (sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2)* (diff( arctan(AiryAi(1, x)/AiryBi(1, x)), x$(1) ))^(2) = (diff( sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2), x$(1) ))^(2)+ (Pi)^(- 2)* (x)^(2)* (sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(- 2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2], {x, 1}])^(2)+ (Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(2)* (D[ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]], {x, 1}])^(2) == (D[Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2], {x, 1}])^(2)+ (Pi)^(- 2)* (x)^(2)* (Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(- 2)</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
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| |-
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| | [https://dlmf.nist.gov/9.8.E17 9.8.E17] || [[Item:Q2851|<math>\tan@{\Airyphasetheta@{x}-\Airyphasederivphi@{x}} = 1/(\pi\AirymodM@{x}\AirymodM'@{x})</math>]] || <math></math> || <syntaxhighlight lang=mathematica>tan(arctan(AiryAi(x)/AiryBi(x))- arctan(AiryAi(1, x)/AiryBi(1, x))) = 1/(Pi*sqrt(AiryAi(x)^2+AiryBi(x)^2)*diff( sqrt(AiryAi(x)^2+AiryBi(x)^2), x$(1) ))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Tan[ArcTan[Divide[AiryAi[x], AiryBi[x]]]- ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]] == 1/(Pi*Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*D[Sqrt[AiryAi[x]^2 + AiryBi[x]^2], {x, 1}])</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
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| |-
| |
| | [https://dlmf.nist.gov/9.8.E17 9.8.E17] || [[Item:Q2851|<math>1/(\pi\AirymodM@{x}\AirymodM'@{x}) = -\AirymodM@{x}\Airyphasetheta'@{x}/\AirymodM'@{x}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>1/(Pi*sqrt(AiryAi(x)^2+AiryBi(x)^2)*diff( sqrt(AiryAi(x)^2+AiryBi(x)^2), x$(1) )) = - sqrt(AiryAi(x)^2+AiryBi(x)^2)*diff( arctan(AiryAi(x)/AiryBi(x)), x$(1) )/diff( sqrt(AiryAi(x)^2+AiryBi(x)^2), x$(1) )</syntaxhighlight> || <syntaxhighlight lang=mathematica>1/(Pi*Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*D[Sqrt[AiryAi[x]^2 + AiryBi[x]^2], {x, 1}]) == - Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*D[ArcTan[Divide[AiryAi[x], AiryBi[x]]], {x, 1}]/D[Sqrt[AiryAi[x]^2 + AiryBi[x]^2], {x, 1}]</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
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| |-
| |
| | [https://dlmf.nist.gov/9.8#Ex4 9.8#Ex4] || [[Item:Q2852|<math>\AirymodM''@{x} = x\AirymodM@{x}+\pi^{-2}\AirymodM^{-3}@{x}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff( sqrt(AiryAi(x)^2+AiryBi(x)^2), x$(2) ) = x*sqrt(AiryAi(x)^2+AiryBi(x)^2)+ (Pi)^(- 2)* (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(- 3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Sqrt[AiryAi[x]^2 + AiryBi[x]^2], {x, 2}] == x*Sqrt[AiryAi[x]^2 + AiryBi[x]^2]+ (Pi)^(- 2)* (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(- 3)</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
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| |-
| |
| | [https://dlmf.nist.gov/9.8#Ex5 9.8#Ex5] || [[Item:Q2853|<math>\AirymodM^{2}'''@{x}-4x\AirymodM^{2}'@{x}-2\AirymodM^{2}@{x} = 0</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff( sqrt(AiryAi(x)^2+AiryBi(x)^2), x$(3) ))^(2)- 4*x*(diff( sqrt(AiryAi(x)^2+AiryBi(x)^2), x$(1) ))^(2)- 2*(sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[Sqrt[AiryAi[x]^2 + AiryBi[x]^2], {x, 3}])^(2)- 4*x*(D[Sqrt[AiryAi[x]^2 + AiryBi[x]^2], {x, 1}])^(2)- 2*(Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2) == 0</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -6.622186001
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| Test Values: {x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.215136643
| |
| Test Values: {x = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -6.622186137209987
| |
| Test Values: {Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.2151366442842328
| |
| Test Values: {Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/9.8.E19 9.8.E19] || [[Item:Q2854|<math>\Airyphasetheta'^{2}@{x}+\tfrac{1}{2}(\Airyphasetheta'''@{x}/\Airyphasetheta'@{x})-\tfrac{3}{4}(\Airyphasetheta''@{x}/\Airyphasetheta'@{x})^{2} = -x</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff( arctan(AiryAi(x)/AiryBi(x)), x$(1) ))^(2)+(1)/(2)*(diff( arctan(AiryAi(x)/AiryBi(x)), x$(3) )/diff( arctan(AiryAi(x)/AiryBi(x)), x$(1) ))-(3)/(4)*(diff( arctan(AiryAi(x)/AiryBi(x)), x$(2) )/diff( arctan(AiryAi(x)/AiryBi(x)), x$(1) ))^(2) = - x</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[ArcTan[Divide[AiryAi[x], AiryBi[x]]], {x, 1}])^(2)+Divide[1,2]*(D[ArcTan[Divide[AiryAi[x], AiryBi[x]]], {x, 3}]/D[ArcTan[Divide[AiryAi[x], AiryBi[x]]], {x, 1}])-Divide[3,4]*(D[ArcTan[Divide[AiryAi[x], AiryBi[x]]], {x, 2}]/D[ArcTan[Divide[AiryAi[x], AiryBi[x]]], {x, 1}])^(2) == - x</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>int(AiryAi(t), t = z..infinity) = Pi*(AiryAi(z)*diff( AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z))), z$(1) )- diff( AiryAi(z), z$(1) )*AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[AiryAi[t], {t, z, Infinity}, GenerateConditions->None] == Pi*(AiryAi[z]*D[ScorerGi[z], {z, 1}]- D[AiryAi[z], {z, 1}]*ScorerGi[z])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3430999769-.7863536809e-1*I
| |
| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1173558541-.6113539683*I
| |
| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>int(AiryAi(t), t = - infinity..z) = Pi*(AiryAi(z)*diff( AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z))), z$(1) )- diff( AiryAi(z), z$(1) )*AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[AiryAi[t], {t, - Infinity, z}, GenerateConditions->None] == Pi*(AiryAi[z]*D[ScorerHi[z], {z, 1}]- D[AiryAi[z], {z, 1}]*ScorerHi[z])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .3430999769+.7863536803e-1*I
| |
| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1173558550+.6113539681*I
| |
| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
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| |
| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>int(AiryBi(t), t = - infinity..z) = int(AiryBi(t), t = 0..z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[AiryBi[t], {t, - Infinity, z}, GenerateConditions->None] == Integrate[AiryBi[t], {t, 0, z}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.10.E3 9.10.E3] || [[Item:Q2885|<math>\int_{0}^{z}\AiryBi@{t}\diff{t} = \pi\left(\AiryBi'@{z}\ScorerGi@{z}-\AiryBi@{z}\ScorerGi'@{z}\right)\\</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int(AiryBi(t), t = 0..z) = Pi*(diff( AiryBi(z), z$(1) )*AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))- AiryBi(z)*diff( AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z))), z$(1) ))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[AiryBi[t], {t, 0, z}, GenerateConditions->None] == Pi*(D[AiryBi[z], {z, 1}]*ScorerGi[z]- AiryBi[z]*D[ScorerGi[z], {z, 1}])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2028158445+.1550535689*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5468682154-.3940689299*I
| |
| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
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| |
| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>Pi*(diff( AiryBi(z), z$(1) )*AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))- AiryBi(z)*diff( AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z))), z$(1) )) = Pi*(AiryBi(z)*diff( AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z))), z$(1) )- diff( AiryBi(z), z$(1) )*AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Pi*(D[AiryBi[z], {z, 1}]*ScorerGi[z]- AiryBi[z]*D[ScorerGi[z], {z, 1}]) == Pi*(AiryBi[z]*D[ScorerHi[z], {z, 1}]- D[AiryBi[z], {z, 1}]*ScorerHi[z])</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .843931870+.115991466*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.9844521300+1.906824069*I
| |
| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
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| |
| | [https://dlmf.nist.gov/9.10#Ex1 9.10#Ex1] || [[Item:Q2893|<math>\int_{0}^{\infty}\AiryAi@{t}\diff{t} = \tfrac{1}{3}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int(AiryAi(t), t = 0..infinity) = (1)/(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[AiryAi[t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,3]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.10#Ex2 9.10#Ex2] || [[Item:Q2894|<math>\int_{-\infty}^{0}\AiryAi@{t}\diff{t} = \tfrac{2}{3}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int(AiryAi(t), t = - infinity..0) = (2)/(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[AiryAi[t], {t, - Infinity, 0}, GenerateConditions->None] == Divide[2,3]</syntaxhighlight> || Failure || Successful || Skip - No test values generated || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.10.E12 9.10.E12] || [[Item:Q2895|<math>\int_{-\infty}^{0}\AiryBi@{t}\diff{t} = 0</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int(AiryBi(t), t = - infinity..0) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[AiryBi[t], {t, - Infinity, 0}, GenerateConditions->None] == 0</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
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| | [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>]] || <math>\Re p > 0</math> || <syntaxhighlight lang=mathematica>int(exp(p*t)*AiryAi(t), t = - infinity..infinity) = exp((p)^(3)/3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[p*t]*AiryAi[t], {t, - Infinity, Infinity}, GenerateConditions->None] == Exp[(p)^(3)/3]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 5] || Skipped - Because timed out
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| | [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>]] || <math>\realpart@@{\tfrac{4}{3}} > 0, \realpart@@{\tfrac{5}{3}} > 0</math> || <syntaxhighlight lang=mathematica>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))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[- p*t]*AiryAi[t], {t, 0, Infinity}, GenerateConditions->None] == 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]]])</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
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| | [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>]] || <math>\Re p > 0, \realpart@@{\tfrac{1}{3}} > 0, \realpart@@{\tfrac{2}{3}} > 0</math> || <syntaxhighlight lang=mathematica>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))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[- p*t]*AiryAi[- t], {t, 0, Infinity}, GenerateConditions->None] == 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]]])</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 5]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1e-9+.6037469539*I
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| Test Values: {p = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br></div></div> || Skipped - Because timed out
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| | [https://dlmf.nist.gov/9.10.E16 9.10.E16] || [[Item:Q2899|<math>\int_{0}^{\infty}e^{-pt}\AiryBi@{-t}\diff{t} = {\frac{1}{\sqrt{3}}e^{p^{3}/3}\left(\frac{\incGamma@{\tfrac{2}{3}}{\tfrac{1}{3}p^{3}}}{\EulerGamma@{\tfrac{2}{3}}}-\frac{\incGamma@{\tfrac{1}{3}}{\tfrac{1}{3}p^{3}}}{\EulerGamma@{\tfrac{1}{3}}}\right)}</math>]] || <math>\Re p > 0, \realpart@@{\tfrac{2}{3}} > 0, \realpart@@{\tfrac{1}{3}} > 0</math> || <syntaxhighlight lang=mathematica>int(exp(- p*t)*AiryBi(- t), t = 0..infinity) = (1)/(sqrt(3))*exp((p)^(3)/3)*((GAMMA((2)/(3), (1)/(3)*(p)^(3)))/(GAMMA((2)/(3)))-(GAMMA((1)/(3), (1)/(3)*(p)^(3)))/(GAMMA((1)/(3))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[- p*t]*AiryBi[- t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,Sqrt[3]]*Exp[(p)^(3)/3]*(Divide[Gamma[Divide[2,3], Divide[1,3]*(p)^(3)],Gamma[Divide[2,3]]]-Divide[Gamma[Divide[1,3], Divide[1,3]*(p)^(3)],Gamma[Divide[1,3]]])</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 5]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.5e-9-.1692833917*I
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| Test Values: {p = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br></div></div> || Skipped - Because timed out
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| | [https://dlmf.nist.gov/9.10.E18 9.10.E18] || [[Item:Q2901|<math>\AiryAi@{z} = \frac{3z^{5/4}e^{-(2/3)z^{3/2}}}{4\pi}\*\int_{0}^{\infty}\frac{t^{-3/4}e^{-(2/3)t^{3/2}}\AiryAi@{t}}{z^{3/2}+t^{3/2}}\diff{t}</math>]] || <math>|\phase@@{z}| < \tfrac{2}{3}\pi</math> || <syntaxhighlight lang=mathematica>AiryAi(z) = (3*(z)^(5/4)* exp(-(2/3)*(z)^(3/2)))/(4*Pi)* int(((t)^(- 3/4)* exp(-(2/3)*(t)^(3/2))*AiryAi(t))/((z)^(3/2)+ (t)^(3/2)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AiryAi[z] == Divide[3*(z)^(5/4)* Exp[-(2/3)*(z)^(3/2)],4*Pi]* Integrate[Divide[(t)^(- 3/4)* Exp[-(2/3)*(t)^(3/2)]*AiryAi[t],(z)^(3/2)+ (t)^(3/2)], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 5] || Skipped - Because timed out
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| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Error || Skipped - Because timed out
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>int(int(AiryAi(t), t = 0..v), v = 0..x) = x*int(AiryAi(t), t = 0..x)- diff( AiryAi(x), x$(1) )+ subs( temp=0, diff( AiryAi(temp), temp$(1) ) )</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Integrate[AiryAi[t], {t, 0, v}, GenerateConditions->None], {v, 0, x}, GenerateConditions->None] == x*Integrate[AiryAi[t], {t, 0, x}, GenerateConditions->None]- D[AiryAi[x], {x, 1}]+ (D[AiryAi[temp], {temp, 1}]/.temp-> 0)</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>int(int(AiryBi(t), t = 0..v), v = 0..x) = x*int(AiryBi(t), t = 0..x)- diff( AiryBi(x), x$(1) )+ subs( temp=0, diff( AiryBi(temp), temp$(1) ) )</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Integrate[AiryBi[t], {t, 0, v}, GenerateConditions->None], {v, 0, x}, GenerateConditions->None] == x*Integrate[AiryBi[t], {t, 0, x}, GenerateConditions->None]- D[AiryBi[x], {x, 1}]+ (D[AiryBi[temp], {temp, 1}]/.temp-> 0)</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
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| | [https://dlmf.nist.gov/9.11.E1 9.11.E1] || [[Item:Q2908|<math>\deriv[3]{w}{z}-4z\deriv{w}{z}-2w = 0</math>]] || <math>w = w_{1}w_{2}</math> || <syntaxhighlight lang=mathematica>diff(w, [z$(3)])- 4*z*diff(w, z)- 2*w = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 3}]- 4*z*D[w, z]- 2*w == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.732050808-1.000000000*I
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| Test Values: {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.732050808-1.000000000*I
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| Test Values: {w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skip - No test values generated
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| | [https://dlmf.nist.gov/9.11.E2 9.11.E2] || [[Item:Q2909|<math>\Wronskian@{\AiryAi^{2}@{z},\AiryAi@{z}\AiryBi@{z},\AiryBi^{2}@{z}} = 2\pi^{-3}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>((AiryAi(z))^(2))*diff(AiryAi(z)*AiryBi(z), z)-diff((AiryAi(z))^(2), z)*(AiryAi(z)*AiryBi(z)) = 2*(Pi)^(- 3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Wronskian[{(AiryAi[z])^(2), AiryAi[z]*AiryBi[z]}, z] == 2*(Pi)^(- 3)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.6075530626e-1-.7911780259e-2*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1529112816e-1-.8621001058e-1*I
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| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.060755306279053636, -0.0079117802669642]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.015291128133821968, -0.08621001051231339]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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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>]] || <math>x \geq 0</math> || <syntaxhighlight lang=mathematica>(AiryAi(x))^(2) = (1)/(4*Pi*sqrt(3))*int(BesselJ(0, (1)/(12)*(t)^(3)+ x*t)*t, t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(AiryAi[x])^(2) == Divide[1,4*Pi*Sqrt[3]]*Integrate[BesselJ[0, Divide[1,12]*(t)^(3)+ x*t]*t, {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>(AiryAi(z))^(2)+ (AiryBi(z))^(2) = (1)/((Pi)^(3/2))*int(exp(z*t -(1)/(12)*(t)^(3))*(t)^(- 1/2), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.205225893+.8288376548*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.763924327-.1437296879*I
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| Test Values: {z = 1.5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>int((1)/((AiryAi(z))^(2)), z) = Pi*(AiryBi(z))/(AiryAi(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[1,(AiryAi[z])^(2)], z, GenerateConditions->None] == Pi*Divide[AiryBi[z],AiryAi[z]]</syntaxhighlight> || Failure || Successful || Error || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.11.E13 9.11.E13] || [[Item:Q2920|<math>\int\frac{\diff{z}}{\AiryAi@{z}\AiryBi@{z}} = \pi\ln@{\frac{\AiryBi@{z}}{\AiryAi@{z}}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int((1)/(AiryAi(z)*AiryBi(z)), z) = Pi*ln((AiryBi(z))/(AiryAi(z)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[1,AiryAi[z]*AiryBi[z]], z, GenerateConditions->None] == Pi*Log[Divide[AiryBi[z],AiryAi[z]]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[-5.779215712137658, -2.873897613994506], Integrate[Times[Power[AiryAi[Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], -1], Power[AiryBi[Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], -1]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Rule[GenerateConditions, None]]]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.1485658721378681, -3.565476804713019], Integrate[Times[Power[AiryAi[Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], -1], Power[AiryBi[Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], -1]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]], Rule[GenerateConditions, None]]]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>int((AiryAi(z)*AiryBi(z))/(((AiryAi(z))^(2)+ (AiryBi(z))^(2))^(2)), z) = (Pi)/(2)*((AiryBi(z))^(2))/((AiryAi(z))^(2)+ (AiryBi(z))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[AiryAi[z]*AiryBi[z],((AiryAi[z])^(2)+ (AiryBi[z])^(2))^(2)], z, GenerateConditions->None] == Divide[Pi,2]*Divide[(AiryBi[z])^(2),(AiryAi[z])^(2)+ (AiryBi[z])^(2)]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[-1.580056541145603, -0.03880964929600676], Integrate[Times[AiryAi[Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], AiryBi[Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[Plus[Power[AiryAi[Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2], Power[AiryBi[Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]], -2]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Rule[GenerateConditions, None]]]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.9914863532591266, -1.6654177670843742], Integrate[Times[AiryAi[Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], AiryBi[Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Power[Plus[Power[AiryAi[Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], 2], Power[AiryBi[Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], 2]], -2]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]], Rule[GenerateCon</div></div>
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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>]] || <math>\realpart@@{\alpha} > 0, \realpart@@{\frac{1}{3}\alpha+\frac{5}{6}} > 0</math> || <syntaxhighlight lang=mathematica>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)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(t)^(\[Alpha]- 1)* (AiryAi[t])^(2), {t, 0, Infinity}, GenerateConditions->None] == Divide[2*Gamma[\[Alpha]],(Pi)^(1/2)* (12)^((2*\[Alpha]+ 5)/6)* Gamma[Divide[1,3]*\[Alpha]+Divide[5,6]]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
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| Test Values: {Rule[α, 0.5]}</syntaxhighlight><br></div></div>
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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>]] || <math>\realpart@@{@} > 0</math> || <syntaxhighlight lang=mathematica>int((AiryAi(t))^(3), t = - infinity..infinity) = ((GAMMA((1)/(3)))^(2))/(4*(Pi)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(AiryAi[t])^(3), {t, - Infinity, Infinity}, GenerateConditions->None] == Divide[(Gamma[Divide[1,3]])^(2),4*(Pi)^(2)]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| | [https://dlmf.nist.gov/9.11.E17 9.11.E17] || [[Item:Q2924|<math>\int_{-\infty}^{\infty}\AiryAi^{2}@{t}\AiryBi@{t}\diff{t} = \frac{\EulerGamma^{2}@{\frac{1}{3}}}{4\sqrt{3}\pi^{2}}</math>]] || <math>\realpart@@{@} > 0</math> || <syntaxhighlight lang=mathematica>int((AiryAi(t))^(2)* AiryBi(t), t = - infinity..infinity) = ((GAMMA((1)/(3)))^(2))/(4*sqrt(3)*(Pi)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(AiryAi[t])^(2)* AiryBi[t], {t, - Infinity, Infinity}, GenerateConditions->None] == Divide[(Gamma[Divide[1,3]])^(2),4*Sqrt[3]*(Pi)^(2)]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| | [https://dlmf.nist.gov/9.11.E18 9.11.E18] || [[Item:Q2925|<math>\int_{0}^{\infty}\AiryAi^{4}@{t}\diff{t} = \frac{\ln@@{3}}{24\pi^{2}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int((AiryAi(t))^(4), t = 0..infinity) = (ln(3))/(24*(Pi)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(AiryAi[t])^(4), {t, 0, Infinity}, GenerateConditions->None] == Divide[Log[3],24*(Pi)^(2)]</syntaxhighlight> || Failure || Failure || Successful [Tested: 0] || Successful [Tested: 1]
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| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>int((1)/((AiryAi(t))^(2)+ (AiryBi(t))^(2)), t = 0..infinity) = int((t)/((diff( AiryAi(t), t$(1) ))^(2)+ (diff( AiryBi(t), t$(1) ))^(2)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[1,(AiryAi[t])^(2)+ (AiryBi[t])^(2)], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[t,(D[AiryAi[t], {t, 1}])^(2)+ (D[AiryBi[t], {t, 1}])^(2)], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 0] || Successful [Tested: 1]
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>int((t)/((diff( AiryAi(t), t$(1) ))^(2)+ (diff( AiryBi(t), t$(1) ))^(2)), t = 0..infinity) = ((Pi)^(2))/(6)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[t,(D[AiryAi[t], {t, 1}])^(2)+ (D[AiryBi[t], {t, 1}])^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[(Pi)^(2),6]</syntaxhighlight> || Failure || Failure || Successful [Tested: 0] || Successful [Tested: 1]
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)])- z*w = (1)/(Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]- z*w == Divide[1,Pi]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.8183098865-.8660254040*I
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| Test Values: {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5477155179-.5000000004*I
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| Test Values: {w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.8183098861837907, -0.8660254037844386]
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| Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.5477155176006481, -0.49999999999999994]
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| Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ScorerGi[z] == AiryBi[z]*Integrate[AiryAi[t], {t, z, Infinity}, GenerateConditions->None]+ AiryAi[z]*Integrate[AiryBi[t], {t, 0, z}, GenerateConditions->None]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 7]
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| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ScorerHi[z] == AiryBi[z]*Integrate[AiryAi[t], {t, - Infinity, z}, GenerateConditions->None]- AiryAi[z]*Integrate[AiryBi[t], {t, - Infinity, z}, GenerateConditions->None]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.12.E6 9.12.E6] || [[Item:Q2934|<math>\ScorerGi@{0} = \tfrac{1}{2}\ScorerHi@{0}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>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)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ScorerGi[0] == Divide[1,2]*ScorerHi[0]</syntaxhighlight> || Failure || Successful || Skip - No test values generated || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.12.E6 9.12.E6] || [[Item:Q2934|<math>\tfrac{1}{2}\ScorerHi@{0} = \tfrac{1}{3}\AiryBi@{0}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(1)/(2)*AiryBi(0)*(int(AiryAi(t), t = -infinity .. (0)))-AiryAi(0)*(int(AiryBi(t), t = -infinity .. (0))) = (1)/(3)*AiryBi(0)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,2]*ScorerHi[0] == Divide[1,3]*AiryBi[0]</syntaxhighlight> || Failure || Successful || Skip - No test values generated || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.12.E6 9.12.E6] || [[Item:Q2934|<math>\tfrac{1}{3}\AiryBi@{0} = {1\Big{/}\!\left(3^{7/6}\EulerGamma@{\tfrac{2}{3}}\right)=0.20497\;55424\ldots,}</math>]] || <math>\realpart@@{\tfrac{2}{3}} > 0</math> || <syntaxhighlight lang=mathematica>(1)/(3)*AiryBi(0) = 1/((3)^(7/6)* GAMMA((2)/(3))) = 0.2049755424</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,3]*AiryBi[0] == 1/((3)^(7/6)* Gamma[Divide[2,3]]) == 0.2049755424</syntaxhighlight> || Error || Failure || Skip - symbolical successful subtest || Error
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| | [https://dlmf.nist.gov/9.12.E7 9.12.E7] || [[Item:Q2935|<math>\ScorerGi'@{0} = \tfrac{1}{2}\ScorerHi'@{0}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>subs( temp=0, diff( AiryBi(temp)*(int(AiryAi(t), t = (temp) .. infinity))+AiryAi(temp)*(int(AiryBi(t), t = 0 .. (temp))), temp$(1) ) ) = (1)/(2)*subs( temp=0, diff( AiryBi(temp)*(int(AiryAi(t), t = -infinity .. (temp)))-AiryAi(temp)*(int(AiryBi(t), t = -infinity .. (temp))), temp$(1) ) )</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[ScorerGi[temp], {temp, 1}]/.temp-> 0) == Divide[1,2]*(D[ScorerHi[temp], {temp, 1}]/.temp-> 0)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.12.E7 9.12.E7] || [[Item:Q2935|<math>\tfrac{1}{2}\ScorerHi'@{0} = \tfrac{1}{3}\AiryBi'@{0}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(1)/(2)*subs( temp=0, diff( AiryBi(temp)*(int(AiryAi(t), t = -infinity .. (temp)))-AiryAi(temp)*(int(AiryBi(t), t = -infinity .. (temp))), temp$(1) ) ) = (1)/(3)*subs( temp=0, diff( AiryBi(temp), temp$(1) ) )</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,2]*(D[ScorerHi[temp], {temp, 1}]/.temp-> 0) == Divide[1,3]*(D[AiryBi[temp], {temp, 1}]/.temp-> 0)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.12.E7 9.12.E7] || [[Item:Q2935|<math>\tfrac{1}{3}\AiryBi'@{0} = 1\Big{/}\left(3^{5/6}\EulerGamma@{\tfrac{1}{3}}\right)</math>]] || <math>\realpart@@{\tfrac{1}{3}} > 0</math> || <syntaxhighlight lang=mathematica>(1)/(3)*subs( temp=0, diff( AiryBi(temp), temp$(1) ) ) = 1/((3)^(5/6)* GAMMA((1)/(3)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,3]*(D[AiryBi[temp], {temp, 1}]/.temp-> 0) == 1/((3)^(5/6)* Gamma[Divide[1,3]])</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.12.E7 9.12.E7] || [[Item:Q2935|<math>1\Big{/}\left(3^{5/6}\EulerGamma@{\tfrac{1}{3}}\right) = 0.14942\;94524\ldots</math>]] || <math>\realpart@@{\tfrac{1}{3}} > 0</math> || <syntaxhighlight lang=mathematica>1/((3)^(5/6)* GAMMA((1)/(3))) = 0.1494294524</syntaxhighlight> || <syntaxhighlight lang=mathematica>1/((3)^(5/6)* Gamma[Divide[1,3]]) == 0.1494294524</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/9.12.E11 9.12.E11] || [[Item:Q2939|<math>\ScorerGi@{z}+\ScorerHi@{z} = \AiryBi@{z}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))+ AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z))) = AiryBi(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ScorerGi[z]+ ScorerHi[z] == AiryBi[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.12.E12 9.12.E12] || [[Item:Q2940|<math>\ScorerGi@{z} = \tfrac{1}{2}e^{\pi i/3}\ScorerHi@{ze^{-2\pi i/3}}+\tfrac{1}{2}e^{-\pi i/3}\ScorerHi@{ze^{2\pi i/3}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z))) = (1)/(2)*exp(Pi*I/3)*AiryBi(z*exp(- 2*Pi*I/3))*(int(AiryAi(t), t = -infinity .. (z*exp(- 2*Pi*I/3))))-AiryAi(z*exp(- 2*Pi*I/3))*(int(AiryBi(t), t = -infinity .. (z*exp(- 2*Pi*I/3))))+(1)/(2)*exp(- Pi*I/3)*AiryBi(z*exp(2*Pi*I/3))*(int(AiryAi(t), t = -infinity .. (z*exp(2*Pi*I/3))))-AiryAi(z*exp(2*Pi*I/3))*(int(AiryBi(t), t = -infinity .. (z*exp(2*Pi*I/3))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ScorerGi[z] == Divide[1,2]*Exp[Pi*I/3]*ScorerHi[z*Exp[- 2*Pi*I/3]]+Divide[1,2]*Exp[- Pi*I/3]*ScorerHi[z*Exp[2*Pi*I/3]]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2356545741-.3070803572*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1024598659-.3465846956*I
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| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.12.E13 9.12.E13] || [[Item:Q2941|<math>\ScorerGi@{z} = e^{-\pi i/3}\ScorerHi@{ze^{+ 2\pi i/3}}+ i\AiryAi@{z}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z))) = exp(- Pi*I/3)*AiryBi(z*exp(+ 2*Pi*I/3))*(int(AiryAi(t), t = -infinity .. (z*exp(+ 2*Pi*I/3))))-AiryAi(z*exp(+ 2*Pi*I/3))*(int(AiryBi(t), t = -infinity .. (z*exp(+ 2*Pi*I/3))))+ I*AiryAi(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ScorerGi[z] == Exp[- Pi*I/3]*ScorerHi[z*Exp[+ 2*Pi*I/3]]+ I*AiryAi[z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1900131227-.1739897867*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1844815903-.2874294645*I
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| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.12.E13 9.12.E13] || [[Item:Q2941|<math>\ScorerGi@{z} = e^{+\pi i/3}\ScorerHi@{ze^{- 2\pi i/3}}- i\AiryAi@{z}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z))) = exp(+ Pi*I/3)*AiryBi(z*exp(- 2*Pi*I/3))*(int(AiryAi(t), t = -infinity .. (z*exp(- 2*Pi*I/3))))-AiryAi(z*exp(- 2*Pi*I/3))*(int(AiryBi(t), t = -infinity .. (z*exp(- 2*Pi*I/3))))- I*AiryAi(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ScorerGi[z] == Exp[+ Pi*I/3]*ScorerHi[z*Exp[- 2*Pi*I/3]]- I*AiryAi[z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1672613648-.2485864233*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .590395216e-1-.1022594507*I
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| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.12.E14 9.12.E14] || [[Item:Q2942|<math>\ScorerHi@{z} = e^{+ 2\pi i/3}\ScorerHi@{ze^{+ 2\pi i/3}}+2e^{-\pi i/6}\AiryAi@{ze^{- 2\pi i/3}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z))) = exp(+ 2*Pi*I/3)*AiryBi(z*exp(+ 2*Pi*I/3))*(int(AiryAi(t), t = -infinity .. (z*exp(+ 2*Pi*I/3))))-AiryAi(z*exp(+ 2*Pi*I/3))*(int(AiryBi(t), t = -infinity .. (z*exp(+ 2*Pi*I/3))))+ 2*exp(- Pi*I/6)*AiryAi(z*exp(- 2*Pi*I/3))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ScorerHi[z] == Exp[+ 2*Pi*I/3]*ScorerHi[z*Exp[+ 2*Pi*I/3]]+ 2*Exp[- Pi*I/6]*AiryAi[z*Exp[- 2*Pi*I/3]]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3013591505+.3291123823*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.4978424366-.3195314878*I
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| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.12.E14 9.12.E14] || [[Item:Q2942|<math>\ScorerHi@{z} = e^{- 2\pi i/3}\ScorerHi@{ze^{- 2\pi i/3}}+2e^{+\pi i/6}\AiryAi@{ze^{+ 2\pi i/3}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z))) = exp(- 2*Pi*I/3)*AiryBi(z*exp(- 2*Pi*I/3))*(int(AiryAi(t), t = -infinity .. (z*exp(- 2*Pi*I/3))))-AiryAi(z*exp(- 2*Pi*I/3))*(int(AiryBi(t), t = -infinity .. (z*exp(- 2*Pi*I/3))))+ 2*exp(+ Pi*I/6)*AiryAi(z*exp(+ 2*Pi*I/3))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ScorerHi[z] == Exp[- 2*Pi*I/3]*ScorerHi[z*Exp[- 2*Pi*I/3]]+ 2*Exp[+ Pi*I/6]*AiryAi[z*Exp[+ 2*Pi*I/3]]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .430564314-.2897051813*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1771185635+.1022594505*I
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| Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.12.E15 9.12.E15] || [[Item:Q2943|<math>\ScorerGi@{z} = \frac{3^{-2/3}}{\pi}\*\sum_{k=0}^{\infty}\cos@{\frac{2k-1}{3}\pi}\EulerGamma@{\frac{k+1}{3}}\frac{(3^{1/3}z)^{k}}{k!}</math>]] || <math>\realpart@@{\frac{k+1}{3}} > 0</math> || <syntaxhighlight lang=mathematica>AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z))) = ((3)^(- 2/3))/(Pi)* sum(cos((2*k - 1)/(3)*Pi)*GAMMA((k + 1)/(3))*(((3)^(1/3)* z)^(k))/(factorial(k)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ScorerGi[z] == Divide[(3)^(- 2/3),Pi]* Sum[Cos[Divide[2*k - 1,3]*Pi]*Gamma[Divide[k + 1,3]]*Divide[((3)^(1/3)* z)^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.12.E16 9.12.E16] || [[Item:Q2944|<math>\ScorerGi'@{z} = \frac{3^{-1/3}}{\pi}\*\sum_{k=0}^{\infty}\cos@{\frac{2k+1}{3}\pi}\EulerGamma@{\frac{k+2}{3}}\frac{(3^{1/3}z)^{k}}{k!}</math>]] || <math>\realpart@@{\frac{k+2}{3}} > 0</math> || <syntaxhighlight lang=mathematica>diff( AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z))), z$(1) ) = ((3)^(- 1/3))/(Pi)* sum(cos((2*k + 1)/(3)*Pi)*GAMMA((k + 2)/(3))*(((3)^(1/3)* z)^(k))/(factorial(k)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[ScorerGi[z], {z, 1}] == Divide[(3)^(- 1/3),Pi]* Sum[Cos[Divide[2*k + 1,3]*Pi]*Gamma[Divide[k + 2,3]]*Divide[((3)^(1/3)* z)^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
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| | [https://dlmf.nist.gov/9.12.E17 9.12.E17] || [[Item:Q2945|<math>\ScorerHi@{z} = \frac{3^{-2/3}}{\pi}\sum_{k=0}^{\infty}\EulerGamma@{\frac{k+1}{3}}\frac{(3^{1/3}z)^{k}}{k!}</math>]] || <math>\realpart@@{\frac{k+1}{3}} > 0</math> || <syntaxhighlight lang=mathematica>AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z))) = ((3)^(- 2/3))/(Pi)*sum(GAMMA((k + 1)/(3))*(((3)^(1/3)* z)^(k))/(factorial(k)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ScorerHi[z] == Divide[(3)^(- 2/3),Pi]*Sum[Gamma[Divide[k + 1,3]]*Divide[((3)^(1/3)* z)^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
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| |
| | [https://dlmf.nist.gov/9.12.E18 9.12.E18] || [[Item:Q2946|<math>\ScorerHi'@{z} = \frac{3^{-1/3}}{\pi}\sum_{k=0}^{\infty}\EulerGamma@{\frac{k+2}{3}}\frac{(3^{1/3}z)^{k}}{k!}</math>]] || <math>\realpart@@{\frac{k+2}{3}} > 0</math> || <syntaxhighlight lang=mathematica>diff( AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z))), z$(1) ) = ((3)^(- 1/3))/(Pi)*sum(GAMMA((k + 2)/(3))*(((3)^(1/3)* z)^(k))/(factorial(k)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[ScorerHi[z], {z, 1}] == Divide[(3)^(- 1/3),Pi]*Sum[Gamma[Divide[k + 2,3]]*Divide[((3)^(1/3)* z)^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
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| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ScorerGi[x] == Divide[1,Pi]*Integrate[Sin[Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 1]
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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>]] || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ScorerHi[z] == Divide[1,Pi]*Integrate[Exp[-Divide[1,3]*(t)^(3)+ z*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .4525872086+.6186053865*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.510759173-.1408206709*I
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| Test Values: {z = 1.5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
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| | [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>]] || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Skipped - Because timed out
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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>]] || <math>|\phase@@{z}| < \tfrac{1}{3}\pi</math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 4]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .660208669e-1-.1388055037e-1*I
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| Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .528823090e-1
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| Test Values: {z = 1.5}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 4]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.06602086668543175, -0.01388055052265768]
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| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0.05288230872547964
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| Test Values: {Rule[z, 1.5]}</syntaxhighlight><br>... skip entries to safe data</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>]] || <math>\realpart@@{\tfrac{1}{3}+\tfrac{1}{3}t} > 0, \realpart@@{-t} > 0</math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Manual Skip! || Skipped - Because timed out
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| | [https://dlmf.nist.gov/9.13#Ex7 9.13#Ex7] || [[Item:Q2976|<math>m = n+2</math>]] || <math></math> || <syntaxhighlight lang=mathematica>m = n + 2</syntaxhighlight> || <syntaxhighlight lang=mathematica>m == n + 2</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| | [https://dlmf.nist.gov/9.13#Ex8 9.13#Ex8] || [[Item:Q2977|<math>t = (\tfrac{1}{2}m)^{-2/m}z</math>]] || <math></math> || <syntaxhighlight lang=mathematica>t = ((1)/(2)*m)^(- 2/m)* z</syntaxhighlight> || <syntaxhighlight lang=mathematica>t == (Divide[1,2]*m)^(- 2/m)* z</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| | [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>]] || <math>\realpart@@{\frac{\alpha+1}{\alpha+2}} > 0</math> || <syntaxhighlight lang=mathematica>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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)]</syntaxhighlight> || Failure || Failure || Error || Error
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| | [https://dlmf.nist.gov/9.13.E21 9.13.E21] || [[Item:Q2984|<math>U_{2}(x,\alpha) = (\alpha+2)^{1/(\alpha+2)}\*\EulerGamma@{\frac{\alpha+3}{\alpha+2}}x^{1/2}\BesselJ{1/(\alpha+2)}@{\frac{2}{\alpha+2}x^{(\alpha+2)/2}}</math>]] || <math>\realpart@@{\frac{\alpha+3}{\alpha+2}} > 0</math> || <syntaxhighlight lang=mathematica>U[2](x , alpha) = (alpha + 2)^(1/(alpha + 2))* GAMMA((alpha + 3)/(alpha + 2))*(x)^(1/2)* BesselJ(1/(alpha + 2), (2)/(alpha + 2)*(x)^((alpha + 2)/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[U, 2][x , \[Alpha]] == (\[Alpha]+ 2)^(1/(\[Alpha]+ 2))* Gamma[Divide[\[Alpha]+ 3,\[Alpha]+ 2]]*(x)^(1/2)* BesselJ[1/(\[Alpha]+ 2), Divide[2,\[Alpha]+ 2]*(x)^((\[Alpha]+ 2)/2)]</syntaxhighlight> || Failure || Failure || Error || Error
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| | [https://dlmf.nist.gov/9.13#Ex9 9.13#Ex9] || [[Item:Q2985|<math>\alpha = m-2</math>]] || <math></math> || <syntaxhighlight lang=mathematica>alpha = m - 2</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Alpha] == m - 2</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| | [https://dlmf.nist.gov/9.13#Ex10 9.13#Ex10] || [[Item:Q2986|<math>x = (m/2)^{2/m}t</math>]] || <math></math> || <syntaxhighlight lang=mathematica>x = (m/2)^(2/m)* t</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == (m/2)^(2/m)* t</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| | [https://dlmf.nist.gov/9.13.E23 9.13.E23] || [[Item:Q2987|<math>U_{1}(x,\alpha) = \frac{\pi^{1/2}}{2^{(m+2)/(2m)}\EulerGamma@{1/m}}\left(W_{m}(t)+W_{m}(-t)\right)</math>]] || <math>\realpart@@{1/m} > 0</math> || <syntaxhighlight lang=mathematica>U[1](x , alpha) = ((Pi)^(1/2))/((2)^((m + 2)/(2*m))* GAMMA(1/m))*(W[m](t)+ W[m](- t))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[U, 1][x , \[Alpha]] == Divide[(Pi)^(1/2),(2)^((m + 2)/(2*m))* Gamma[1/m]]*(Subscript[W, m][t]+ Subscript[W, m][- t])</syntaxhighlight> || Failure || Failure || Error || Error
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| | [https://dlmf.nist.gov/9.13.E24 9.13.E24] || [[Item:Q2988|<math>U_{2}(x,\alpha) = \frac{\pi^{1/2}m^{2/m}}{2^{(m+2)/(2m)}\EulerGamma@{-1/m}}\left(W_{m}(t){-}W_{m}(-t)\right)</math>]] || <math>\realpart@@{-1/m} > 0</math> || <syntaxhighlight lang=mathematica>U[2](x , alpha) = ((Pi)^(1/2)* (m)^(2/m))/((2)^((m + 2)/(2*m))* GAMMA(- 1/m))*(W[m](t)- W[m](- t))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[U, 2][x , \[Alpha]] == Divide[(Pi)^(1/2)* (m)^(2/m),(2)^((m + 2)/(2*m))* Gamma[- 1/m]]*(Subscript[W, m][t]- Subscript[W, m][- t])</syntaxhighlight> || Failure || Failure || Error || Error
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| |}
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