Results of Airy and Related Functions: Difference between revisions

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{| class="wikitable sortable" style="margin: 0;"
; Notation : [[9.1|9.1 Special Notation]]<br>
|-
; 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>
! scope="col" style="position: sticky; top: 0;" | DLMF
; 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>
! scope="col" style="position: sticky; top: 0;" | Formula
; Applications : [[9.15|9.15 Mathematical Applications]]<br>[[9.16|9.16 Physical Applications]]<br>
! scope="col" style="position: sticky; top: 0;" | Constraints
; 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>
! scope="col" style="position: sticky; top: 0;" | Maple
! scope="col" style="position: sticky; top: 0;" | Mathematica
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \AiryAi@{z},\;\AiryBi@{z},\;\AiryAi@{ze^{- 2\pi\iunit/3}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w = AiryAi(z); AiryBi(z), AiryAi(z*exp(- 2*Pi*I/3))</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == AiryAi[z]
AiryBi[z], AiryAi[z*Exp[- 2*Pi*I/3]]</syntaxhighlight> || Failure || Failure || Error || Error
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \AiryAi@{z},\;\AiryBi@{z},\;\AiryAi@{ze^{+ 2\pi\iunit/3}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w = AiryAi(z); AiryBi(z), AiryAi(z*exp(+ 2*Pi*I/3))</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == AiryAi[z]
AiryBi[z], AiryAi[z*Exp[+ 2*Pi*I/3]]</syntaxhighlight> || Failure || Failure || Error || Error
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi@{0} = \frac{1}{3^{2/3}\EulerGamma@{\tfrac{2}{3}}}</syntaxhighlight> || <math></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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{3^{2/3}\EulerGamma@{\tfrac{2}{3}}} = 0.35502\;80538\ldots</syntaxhighlight> || <math></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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi'@{0} = -\frac{1}{3^{1/3}\EulerGamma@{\tfrac{1}{3}}}</syntaxhighlight> || <math></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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\frac{1}{3^{1/3}\EulerGamma@{\tfrac{1}{3}}} = -0.25881\;94037\ldots</syntaxhighlight> || <math></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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryBi@{0} = \frac{1}{3^{1/6}\EulerGamma@{\tfrac{2}{3}}}</syntaxhighlight> || <math></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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{3^{1/6}\EulerGamma@{\tfrac{2}{3}}} = 0.61492\;66274\ldots</syntaxhighlight> || <math></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]
|-
| [https://dlmf.nist.gov/9.2.E6 9.2.E6] || [[Item:Q2758|<math>\AiryBi'@{0} = \frac{3^{1/6}}{\EulerGamma@{\tfrac{1}{3}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryBi'@{0} = \frac{3^{1/6}}{\EulerGamma@{\tfrac{1}{3}}}</syntaxhighlight> || <math></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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{3^{1/6}}{\EulerGamma@{\tfrac{1}{3}}} = 0.44828\;83573\ldots</syntaxhighlight> || <math></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]
|-
| [https://dlmf.nist.gov/9.2.E7 9.2.E7] || [[Item:Q2759|<math>\Wronskian@{\AiryAi@{z},\AiryBi@{z}} = \frac{1}{\pi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wronskian@{\AiryAi@{z},\AiryBi@{z}} = \frac{1}{\pi}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wronskian@{\AiryAi@{z},\AiryAi@{ze^{- 2\pi i/3}}} = \frac{e^{+\pi i/6}}{2\pi}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wronskian@{\AiryAi@{z},\AiryAi@{ze^{+ 2\pi i/3}}} = \frac{e^{-\pi i/6}}{2\pi}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wronskian@{\AiryAi@{ze^{-2\pi i/3}},\AiryAi@{ze^{2\pi i/3}}} = \frac{1}{2\pi i}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryBi@{z} = e^{-\pi i/6}\AiryAi@{ze^{-2\pi i/3}}+e^{\pi i/6}\AiryAi@{ze^{2\pi i/3}}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi@{ze^{- 2\pi i/3}} = \tfrac{1}{2}e^{-\pi i/3}\left(\AiryAi@{z}+ i\AiryBi@{z}\right)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi@{ze^{+ 2\pi i/3}} = \tfrac{1}{2}e^{+\pi i/3}\left(\AiryAi@{z}- i\AiryBi@{z}\right)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi@{-z} = e^{\pi i/3}\AiryAi@{ze^{\pi i/3}}+e^{-\pi i/3}\AiryAi@{ze^{-\pi i/3}}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryBi@{-z} = e^{-\pi i/6}\AiryAi@{ze^{\pi i/3}}+e^{\pi i/6}\AiryAi@{ze^{-\pi i/3}}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi@{x} = \frac{1}{\pi}\int_{0}^{\infty}\cos@{\tfrac{1}{3}t^{3}+xt}\diff{t}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <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
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <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
Test Values: {x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2865429290-.9608783696e-1*I
Test Values: {x = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 3]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <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
Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5566528573-.2432725641*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: 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]]]]
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]]]]
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>... skip entries to safe data</div></div>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <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
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi@{z} = \frac{\sqrt{3}}{2\pi}\int_{0}^{\infty}\exp@{-\frac{t^{3}}{3}-\frac{z^{3}}{3t^{3}}}\diff{t}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi@{z} = \frac{e^{-\zeta}}{\pi}\int_{0}^{\infty}\exp@{-z^{\ifrac{1}{2}}t^{2}}\cos@{\tfrac{1}{3}t^{3}}\diff{t}</syntaxhighlight> || <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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <math>|\phase@@{z}| < \frac{2}{3}\pi</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
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]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/9.6.E2 9.6.E2] || [[Item:Q2782|<math>\AiryAi@{z} = \pi^{-1}\sqrt{z/3}\modBesselK{+ 1/3}@{\zeta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi@{z} = \pi^{-1}\sqrt{z/3}\modBesselK{+ 1/3}@{\zeta}</syntaxhighlight> || <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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi@{z} = \pi^{-1}\sqrt{z/3}\modBesselK{- 1/3}@{\zeta}</syntaxhighlight> || <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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pi^{-1}\sqrt{z/3}\modBesselK{+ 1/3}@{\zeta} = \tfrac{1}{3}\sqrt{z}\left(\modBesselI{-1/3}@{\zeta}-\modBesselI{1/3}@{\zeta}\right)</syntaxhighlight> || <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>\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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pi^{-1}\sqrt{z/3}\modBesselK{- 1/3}@{\zeta} = \tfrac{1}{3}\sqrt{z}\left(\modBesselI{-1/3}@{\zeta}-\modBesselI{1/3}@{\zeta}\right)</syntaxhighlight> || <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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}</syntaxhighlight> || <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
Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.028202948-.1796919595*I
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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}</syntaxhighlight> || <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
Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4467028535+.6697146486*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 [3 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.0456595063579188, 0.6037117974764359]
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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi'@{z} = -\pi^{-1}(z/\sqrt{3})\modBesselK{+ 2/3}@{\zeta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff( AiryAi(z), z$(1) ) = - (Pi)^(- 1)*(z/(sqrt(3)))*BesselK(+ 2/3, (2)/(3)*(z)^((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[AiryAi[z], {z, 1}] == - (Pi)^(- 1)*(z/(Sqrt[3]))*BesselK[+ 2/3, Divide[2,3]*(z)^(Divide[3,2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2876791930+.6573919010*I
Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.2876791932746734, 0.657391901009072]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
|-
| [https://dlmf.nist.gov/9.6.E3 9.6.E3] || [[Item:Q2783|<math>\AiryAi'@{z} = -\pi^{-1}(z/\sqrt{3})\modBesselK{- 2/3}@{\zeta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi'@{z} = -\pi^{-1}(z/\sqrt{3})\modBesselK{- 2/3}@{\zeta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff( AiryAi(z), z$(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
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]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\pi^{-1}(z/\sqrt{3})\modBesselK{+ 2/3}@{\zeta} = (z/3)\left(\modBesselI{2/3}@{\zeta}-\modBesselI{-2/3}@{\zeta}\right)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\pi^{-1}(z/\sqrt{3})\modBesselK{- 2/3}@{\zeta} = (z/3)\left(\modBesselI{2/3}@{\zeta}-\modBesselI{-2/3}@{\zeta}\right)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(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}}</syntaxhighlight> || <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
Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2876791931-.6573919012*I
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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}</syntaxhighlight> || <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
Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2641265961-.1348949430*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 [3 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8075132057195987, 0.46621796669638804]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.26412659586991316, -0.13489494274589095]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/9.6.E3 9.6.E3] || [[Item:Q2783|<math>\tfrac{1}{2}(z/\sqrt{3})e^{\pi i/6}\HankelH{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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryBi@{z} = \sqrt{z/3}\left(\modBesselI{1/3}@{\zeta}+\modBesselI{-1/3}@{\zeta}\right)</syntaxhighlight> || <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
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]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
|-
| [https://dlmf.nist.gov/9.6.E4 9.6.E4] || [[Item:Q2784|<math>\sqrt{z/3}\left(\modBesselI{1/3}@{\zeta}+\modBesselI{-1/3}@{\zeta}\right) = \tfrac{1}{2}\sqrt{z/3}\left(e^{\pi i/6}\HankelH{1}{1/3}@{\zeta e^{-\pi i/2}}+e^{-\pi i/6}\HankelH{2}{1/3}@{\zeta e^{\pi i/2}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)</syntaxhighlight> || <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
Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.199319247+.6472196920e-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[1.1856739752313228, 0.06468773371996589]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.1993192456185722, 0.06472196909084393]
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.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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryBi'@{z} = (z/\sqrt{3})\left(\modBesselI{2/3}@{\zeta}+\modBesselI{-2/3}@{\zeta}\right)</syntaxhighlight> || <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
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]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
|-
| [https://dlmf.nist.gov/9.6.E5 9.6.E5] || [[Item:Q2785|<math>(z/\sqrt{3})\left(\modBesselI{2/3}@{\zeta}+\modBesselI{-2/3}@{\zeta}\right) = \tfrac{1}{2}(z/\sqrt{3})\left(e^{\pi i/3}\HankelH{1}{2/3}@{\zeta e^{-\pi i/2}}+e^{-\pi i/3}\HankelH{2}{2/3}@{\zeta e^{\pi i/2}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(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)</syntaxhighlight> || <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
Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .6988938865-.1407017700*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[0.7341782376555157, 0.19166014735752115]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.6988938863252578, -0.14070176990144198]
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.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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi@{-z} = (\sqrt{z}/3)\left(\BesselJ{1/3}@{\zeta}+\BesselJ{-1/3}@{\zeta}\right)</syntaxhighlight> || <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
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]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(\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)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi'@{-z} = (z/3)\left(\BesselJ{2/3}@{\zeta}-\BesselJ{-2/3}@{\zeta}\right)</syntaxhighlight> || <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
Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4379687237+.3495995698*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[0.7438814497662649, -0.18248307701953514]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.4379687237504881, 0.3495995697137311]
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.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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(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)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryBi@{-z} = \sqrt{z/3}\left(\BesselJ{-1/3}@{\zeta}-\BesselJ{1/3}@{\zeta}\right)</syntaxhighlight> || <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
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]
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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryBi'@{-z} = (z/\sqrt{3})\left(\BesselJ{-2/3}@{\zeta}+\BesselJ{2/3}@{\zeta}\right)</syntaxhighlight> || <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
Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5604204721-.1077527266*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[-0.4079506515473492, -0.40011993153434466]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.5604204722153456, -0.10775272665850918]
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.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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(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)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BesselJ{+ 1/3}@{\zeta} = \tfrac{1}{2}\sqrt{3/z}\left(\sqrt{3}\AiryAi@{-z}-\AiryBi@{-z}\right)</syntaxhighlight> || <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
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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BesselJ{- 1/3}@{\zeta} = \tfrac{1}{2}\sqrt{3/z}\left(\sqrt{3}\AiryAi@{-z}+\AiryBi@{-z}\right)</syntaxhighlight> || <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
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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BesselJ{+ 2/3}@{\zeta} = \tfrac{1}{2}(\sqrt{3}/z)\left(+\sqrt{3}\AiryAi'@{-z}+\AiryBi'@{-z}\right)</syntaxhighlight> || <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$(1) ) ))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselJ[+ 2/3, Divide[2,3]*(z)^(Divide[3,2])] == Divide[1,2]*(Sqrt[3]/z)*(+Sqrt[3]*(D[AiryAi[temp], {temp, 1}]/.temp-> - z)+ (D[AiryBi[temp], {temp, 1}]/.temp-> - z))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .4073114590+.8284435869*I
Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.40731145887570114, 0.8284435866207246]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
|-
| [https://dlmf.nist.gov/9.6.E12 9.6.E12] || [[Item:Q2792|<math>\BesselJ{- 2/3}@{\zeta} = \tfrac{1}{2}(\sqrt{3}/z)\left(-\sqrt{3}\AiryAi'@{-z}+\AiryBi'@{-z}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BesselJ{- 2/3}@{\zeta} = \tfrac{1}{2}(\sqrt{3}/z)\left(-\sqrt{3}\AiryAi'@{-z}+\AiryBi'@{-z}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BesselJ(- 2/3, (2)/(3)*(z)^((3)/(2))) = (1)/(2)*(sqrt(3)/z)*(-sqrt(3)*subs( temp=- z, diff( AiryAi(temp), temp$(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
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]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{+ 1/3}@{\zeta} = \tfrac{1}{2}\sqrt{3/z}\left(-\sqrt{3}\AiryAi@{z}+\AiryBi@{z}\right)</syntaxhighlight> || <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]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{- 1/3}@{\zeta} = \tfrac{1}{2}\sqrt{3/z}\left(+\sqrt{3}\AiryAi@{z}+\AiryBi@{z}\right)</syntaxhighlight> || <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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{+ 2/3}@{\zeta} = \tfrac{1}{2}(\sqrt{3}/z)\left(+\sqrt{3}\AiryAi'@{z}+\AiryBi'@{z}\right)</syntaxhighlight> || <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$(1) ))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[+ 2/3, Divide[2,3]*(z)^(Divide[3,2])] == Divide[1,2]*(Sqrt[3]/z)*(+Sqrt[3]*D[AiryAi[z], {z, 1}]+ D[AiryBi[z], {z, 1}])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5137974625+.7669638641*I
Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.5137974621779913, 0.7669638639492199]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
|-
| [https://dlmf.nist.gov/9.6.E14 9.6.E14] || [[Item:Q2794|<math>\modBesselI{- 2/3}@{\zeta} = \tfrac{1}{2}(\sqrt{3}/z)\left(-\sqrt{3}\AiryAi'@{z}+\AiryBi'@{z}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{- 2/3}@{\zeta} = \tfrac{1}{2}(\sqrt{3}/z)\left(-\sqrt{3}\AiryAi'@{z}+\AiryBi'@{z}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BesselI(- 2/3, (2)/(3)*(z)^((3)/(2))) = (1)/(2)*(sqrt(3)/z)*(-sqrt(3)*diff( AiryAi(z), z$(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>
|-
| [https://dlmf.nist.gov/9.6.E15 9.6.E15] || [[Item:Q2795|<math>\modBesselK{+ 1/3}@{\zeta} = \pi\sqrt{3/z}\AiryAi@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{+ 1/3}@{\zeta} = \pi\sqrt{3/z}\AiryAi@{z}</syntaxhighlight> || <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.E15 9.6.E15] || [[Item:Q2795|<math>\modBesselK{- 1/3}@{\zeta} = \pi\sqrt{3/z}\AiryAi@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{- 1/3}@{\zeta} = \pi\sqrt{3/z}\AiryAi@{z}</syntaxhighlight> || <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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{+ 2/3}@{\zeta} = -\pi(\sqrt{3}/z)\AiryAi'@{z}</syntaxhighlight> || <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.E16 9.6.E16] || [[Item:Q2796|<math>\modBesselK{- 2/3}@{\zeta} = -\pi(\sqrt{3}/z)\AiryAi'@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{- 2/3}@{\zeta} = -\pi(\sqrt{3}/z)\AiryAi'@{z}</syntaxhighlight> || <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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\HankelH{1}{1/3}@{\zeta} = e^{-\pi i/3}\HankelH{1}{-1/3}@{\zeta}</syntaxhighlight> || <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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>e^{-\pi i/3}\HankelH{1}{-1/3}@{\zeta} = e^{-\pi i/6}\sqrt{3/z}\left(\AiryAi@{-z}-i\AiryBi@{-z}\right)</syntaxhighlight> || <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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\HankelH{1}{2/3}@{\zeta} = e^{-2\pi i/3}\HankelH{1}{-2/3}@{\zeta}</syntaxhighlight> || <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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>e^{-2\pi i/3}\HankelH{1}{-2/3}@{\zeta} = e^{\pi i/6}(\sqrt{3}/z)\left(\AiryAi'@{-z}-i\AiryBi'@{-z}\right)</syntaxhighlight> || <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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\HankelH{2}{1/3}@{\zeta} = e^{\pi i/3}\HankelH{2}{-1/3}@{\zeta}</syntaxhighlight> || <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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>e^{\pi i/3}\HankelH{2}{-1/3}@{\zeta} = e^{\pi i/6}\sqrt{3/z}\left(\AiryAi@{-z}+i\AiryBi@{-z}\right)</syntaxhighlight> || <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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\HankelH{2}{2/3}@{\zeta} = e^{2\pi i/3}\HankelH{2}{-2/3}@{\zeta}</syntaxhighlight> || <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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>e^{2\pi i/3}\HankelH{2}{-2/3}@{\zeta} = e^{-\pi i/6}(\sqrt{3}/z)\left(\AiryAi'@{-z}+i\AiryBi'@{-z}\right)</syntaxhighlight> || <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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi@{z} = \tfrac{1}{2}\pi^{-1/2}z^{-1/4}\WhittakerconfhyperW{0}{1/3}@{2\zeta}</syntaxhighlight> || <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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi'@{z} = -\tfrac{1}{2}\pi^{-1/2}z^{1/4}\WhittakerconfhyperW{0}{2/3}@{2\zeta}</syntaxhighlight> || <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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\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}</syntaxhighlight> || <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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <math></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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <math></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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <math></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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <math></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>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/9.7#Ex2 9.7#Ex2] || [[Item:Q2809|<math>v_{k} = \frac{6k+1}{1-6k}u_{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>v_{k} = \frac{6k+1}{1-6k}u_{k}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">v[k] = (6*k + 1)/(1 - 6*k)*u[k]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[v, k] == Divide[6*k + 1,1 - 6*k]*Subscript[u, k]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi@{x} \leq \frac{e^{-\xi}}{2\sqrt{\pi}x^{1/4}}</syntaxhighlight> || <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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>|\AiryAi'@{x}| \leq \frac{x^{1/4}e^{-\xi}}{2\sqrt{\pi}}\left(1+\frac{7}{72\xi}\right)</syntaxhighlight> || <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
Test Values: {x = 1.5, xi = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .9738201284e-1 <= .4430404444e-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[0.0973820128423013, 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]]
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/9.7#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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)</syntaxhighlight> || <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
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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryBi'@{x} \leq \frac{x^{1/4}e^{\xi}}{\sqrt{\pi}}\left(1+\left(\frac{\cpi}{2}+1\right)\frac{7}{72\xi}\right)</syntaxhighlight> || <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
Test Values: {x = 1.5, xi = -1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.886212255 <= .1893988815
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]]
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]]
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/9.7.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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)</syntaxhighlight> || <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
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
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
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)</syntaxhighlight> || <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
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
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\scterminant{p}@{z} = \frac{e^{z}}{2\pi}\EulerGamma@{p}\incGamma@{1-p}{z}</syntaxhighlight> || <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 || - || -
|-
| [https://dlmf.nist.gov/9.8.E1 9.8.E1] || [[Item:Q2833|<math>\AiryAi@{x} = \AirymodM@{x}\sin@@{\Airyphasetheta@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi@{x} = \AirymodM@{x}\sin@@{\Airyphasetheta@{x}}</syntaxhighlight> || <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]
|-
| [https://dlmf.nist.gov/9.8.E2 9.8.E2] || [[Item:Q2834|<math>\AiryBi@{x} = \AirymodM@{x}\cos@@{\Airyphasetheta@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryBi@{x} = \AirymodM@{x}\cos@@{\Airyphasetheta@{x}}</syntaxhighlight> || <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]
|-
| [https://dlmf.nist.gov/9.8.E3 9.8.E3] || [[Item:Q2835|<math>\AirymodM@{x} = \sqrt{\AiryAi^{2}@{x}+\AiryBi^{2}@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AirymodM@{x} = \sqrt{\AiryAi^{2}@{x}+\AiryBi^{2}@{x}}</syntaxhighlight> || <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]
|-
| [https://dlmf.nist.gov/9.8.E4 9.8.E4] || [[Item:Q2836|<math>\Airyphasetheta@{x} = \atan@{\AiryAi@{x}/\AiryBi@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Airyphasetheta@{x} = \atan@{\AiryAi@{x}/\AiryBi@{x}}</syntaxhighlight> || <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]
|-
| [https://dlmf.nist.gov/9.8.E5 9.8.E5] || [[Item:Q2837|<math>\AiryAi'@{x} = \AirymodderivN@{x}\sin@@{\Airyphasederivphi@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi'@{x} = \AirymodderivN@{x}\sin@@{\Airyphasederivphi@{x}}</syntaxhighlight> || <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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryBi'@{x} = \AirymodderivN@{x}\cos@@{\Airyphasederivphi@{x}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff( AiryBi(x), x$(1) ) = sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2)*cos(arctan(AiryAi(1, x)/AiryBi(1, x)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[AiryBi[x], {x, 1}] == Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2]*Cos[ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
|-
| [https://dlmf.nist.gov/9.8.E7 9.8.E7] || [[Item:Q2839|<math>\AirymodderivN@{x} = \sqrt{\AiryAi'^{2}@{x}+\AiryBi'^{2}@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AirymodderivN@{x} = \sqrt{\AiryAi'^{2}@{x}+\AiryBi'^{2}@{x}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2) = sqrt((diff( AiryAi(x), x$(1) ))^(2)+ (diff( AiryBi(x), x$(1) ))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2] == Sqrt[(D[AiryAi[x], {x, 1}])^(2)+ (D[AiryBi[x], {x, 1}])^(2)]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
|-
| [https://dlmf.nist.gov/9.8.E8 9.8.E8] || [[Item:Q2840|<math>\Airyphasederivphi@{x} = \atan@{\AiryAi'@{x}/\AiryBi'@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Airyphasederivphi@{x} = \atan@{\AiryAi'@{x}/\AiryBi'@{x}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctan(AiryAi(1, x)/AiryBi(1, x)) = arctan(diff( AiryAi(x), x$(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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>|x|^{1/2}\AirymodM^{2}@{x} = \tfrac{1}{2}\xi\left(\BesselJ{1/3}^{2}@{\xi}+\BesselY{1/3}^{2}@{\xi}\right)</syntaxhighlight> || <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
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
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]
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]
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.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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>|x|^{-1/2}\AirymodderivN^{2}@{x} = \tfrac{1}{2}\xi\left(\BesselJ{2/3}^{2}@{\xi}+\BesselY{2/3}^{2}@{\xi}\right)</syntaxhighlight> || <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
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
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]
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]
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.E11 9.8.E11] || [[Item:Q2843|<math>\Airyphasetheta@{x} = \tfrac{2}{3}\pi+\atan@{\BesselY{1/3}@{\xi}/\BesselJ{1/3}@{\xi}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Airyphasetheta@{x} = \tfrac{2}{3}\pi+\atan@{\BesselY{1/3}@{\xi}/\BesselJ{1/3}@{\xi}}</syntaxhighlight> || <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
Test Values: {x = 1.5, xi = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.390111334-.9722564139*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[-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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Airyphasederivphi@{x} = \tfrac{1}{3}\pi+\atan@{\BesselY{2/3}@{\xi}/\BesselJ{2/3}@{\xi}}</syntaxhighlight> || <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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AirymodM@{x}\AirymodderivN@{x}\sin@{\Airyphasetheta@{x}-\Airyphasederivphi@{x}} = \pi^{-1}</syntaxhighlight> || <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]
|-
| [https://dlmf.nist.gov/9.8#Ex1 9.8#Ex1] || [[Item:Q2846|<math>\AirymodM^{2}@{x}\Airyphasetheta'@{x} = -\pi^{-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AirymodM^{2}@{x}\Airyphasetheta'@{x} = -\pi^{-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)* diff( arctan(AiryAi(x)/AiryBi(x)), x$(1) ) = - (Pi)^(- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)* D[ArcTan[Divide[AiryAi[x], AiryBi[x]]], {x, 1}] == - (Pi)^(- 1)</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
|-
| [https://dlmf.nist.gov/9.8#Ex2 9.8#Ex2] || [[Item:Q2847|<math>\AirymodderivN^{2}@{x}\Airyphasederivphi'@{x} = \pi^{-1}x</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AirymodderivN^{2}@{x}\Airyphasederivphi'@{x} = \pi^{-1}x</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2)* diff( arctan(AiryAi(1, x)/AiryBi(1, x)), x$(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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AirymodderivN@{x}\AirymodderivN'@{x} = x\AirymodM@{x}\AirymodM'@{x}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AirymodderivN^{2}@{x} = \AirymodM'^{2}@{x}+\AirymodM^{2}@{x}\Airyphasetheta'^{2}@{x}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AirymodM'^{2}@{x}+\AirymodM^{2}@{x}\Airyphasetheta'^{2}@{x} = \AirymodM'^{2}(x)+\pi^{-2}\AirymodM^{-2}@{x}</syntaxhighlight> || <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$(1) ) ))^(2)+ (Pi)^(- 2)* (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(- 2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[Sqrt[AiryAi[x]^2 + AiryBi[x]^2], {x, 1}])^(2)+ (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)* (D[ArcTan[Divide[AiryAi[x], AiryBi[x]]], {x, 1}])^(2) == ((D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> (x)))^(2)+ (Pi)^(- 2)* (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(- 2)</syntaxhighlight> || Translation Error || Translation Error || - || -
|-
| [https://dlmf.nist.gov/9.8.E16 9.8.E16] || [[Item:Q2850|<math>x^{2}\AirymodM^{2}@{x} = \AirymodderivN'^{2}@{x}+\AirymodderivN^{2}@{x}\Airyphasederivphi'^{2}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x^{2}\AirymodM^{2}@{x} = \AirymodderivN'^{2}@{x}+\AirymodderivN^{2}@{x}\Airyphasederivphi'^{2}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(x)^(2)* (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2) = (diff( sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2), x$(1) ))^(2)+ (sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2)* (diff( arctan(AiryAi(1, x)/AiryBi(1, x)), x$(1) ))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(x)^(2)* (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2) == (D[Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2], {x, 1}])^(2)+ (Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(2)* (D[ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]], {x, 1}])^(2)</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 3]
|-
| [https://dlmf.nist.gov/9.8.E16 9.8.E16] || [[Item:Q2850|<math>\AirymodderivN'^{2}@{x}+\AirymodderivN^{2}@{x}\Airyphasederivphi'^{2}@{x} = \AirymodderivN'^{2}@{x}+\pi^{-2}x^{2}\AirymodderivN^{-2}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AirymodderivN'^{2}@{x}+\AirymodderivN^{2}@{x}\Airyphasederivphi'^{2}@{x} = \AirymodderivN'^{2}@{x}+\pi^{-2}x^{2}\AirymodderivN^{-2}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(diff( sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2), x$(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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tan@{\Airyphasetheta@{x}-\Airyphasederivphi@{x}} = 1/(\pi\AirymodM@{x}\AirymodM'@{x})</syntaxhighlight> || <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$(1) ))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Tan[ArcTan[Divide[AiryAi[x], AiryBi[x]]]- ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]] == 1/(Pi*Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*D[Sqrt[AiryAi[x]^2 + AiryBi[x]^2], {x, 1}])</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
|-
| [https://dlmf.nist.gov/9.8.E17 9.8.E17] || [[Item:Q2851|<math>1/(\pi\AirymodM@{x}\AirymodM'@{x}) = -\AirymodM@{x}\Airyphasetheta'@{x}/\AirymodM'@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>1/(\pi\AirymodM@{x}\AirymodM'@{x}) = -\AirymodM@{x}\Airyphasetheta'@{x}/\AirymodM'@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>1/(Pi*sqrt(AiryAi(x)^2+AiryBi(x)^2)*diff( sqrt(AiryAi(x)^2+AiryBi(x)^2), x$(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]
|-
| [https://dlmf.nist.gov/9.8#Ex4 9.8#Ex4] || [[Item:Q2852|<math>\AirymodM''@{x} = x\AirymodM@{x}+\pi^{-2}\AirymodM^{-3}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AirymodM''@{x} = x\AirymodM@{x}+\pi^{-2}\AirymodM^{-3}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff( sqrt(AiryAi(x)^2+AiryBi(x)^2), x$(2) ) = x*sqrt(AiryAi(x)^2+AiryBi(x)^2)+ (Pi)^(- 2)* (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(- 3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Sqrt[AiryAi[x]^2 + AiryBi[x]^2], {x, 2}] == x*Sqrt[AiryAi[x]^2 + AiryBi[x]^2]+ (Pi)^(- 2)* (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(- 3)</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
|-
| [https://dlmf.nist.gov/9.8#Ex5 9.8#Ex5] || [[Item:Q2853|<math>\AirymodM^{2}'''@{x}-4x\AirymodM^{2}'@{x}-2\AirymodM^{2}@{x} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AirymodM^{2}'''@{x}-4x\AirymodM^{2}'@{x}-2\AirymodM^{2}@{x} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(diff( sqrt(AiryAi(x)^2+AiryBi(x)^2), x$(3) ))^(2)- 4*x*(diff( sqrt(AiryAi(x)^2+AiryBi(x)^2), x$(1) ))^(2)- 2*(sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[Sqrt[AiryAi[x]^2 + AiryBi[x]^2], {x, 3}])^(2)- 4*x*(D[Sqrt[AiryAi[x]^2 + AiryBi[x]^2], {x, 1}])^(2)- 2*(Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2) == 0</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -6.622186001
Test Values: {x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.215136643
Test Values: {x = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -6.622186137209987
Test Values: {Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.2151366442842328
Test Values: {Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/9.8.E19 9.8.E19] || [[Item:Q2854|<math>\Airyphasetheta'^{2}@{x}+\tfrac{1}{2}(\Airyphasetheta'''@{x}/\Airyphasetheta'@{x})-\tfrac{3}{4}(\Airyphasetheta''@{x}/\Airyphasetheta'@{x})^{2} = -x</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Airyphasetheta'^{2}@{x}+\tfrac{1}{2}(\Airyphasetheta'''@{x}/\Airyphasetheta'@{x})-\tfrac{3}{4}(\Airyphasetheta''@{x}/\Airyphasetheta'@{x})^{2} = -x</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(diff( arctan(AiryAi(x)/AiryBi(x)), x$(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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{z}^{\infty}\AiryAi@{t}\diff{t} = \pi\left(\AiryAi@{z}\ScorerGi'@{z}-\AiryAi'@{z}\ScorerGi@{z}\right)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{-\infty}^{z}\AiryAi@{t}\diff{t} = \pi\left(\AiryAi@{z}\ScorerHi'@{z}-\AiryAi'@{z}\ScorerHi@{z}\right)</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{-\infty}^{z}\AiryBi@{t}\diff{t} = \int_{0}^{z}\AiryBi@{t}\diff{t}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{z}\AiryBi@{t}\diff{t} = \pi\left(\AiryBi'@{z}\ScorerGi@{z}-\AiryBi@{z}\ScorerGi'@{z}\right)\\</syntaxhighlight> || <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
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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pi\left(\AiryBi'@{z}\ScorerGi@{z}-\AiryBi@{z}\ScorerGi'@{z}\right)\\ = \pi\left(\AiryBi@{z}\ScorerHi'@{z}-\AiryBi'@{z}\ScorerHi@{z}\right)</syntaxhighlight> || <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
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]
|-
| [https://dlmf.nist.gov/9.10#Ex1 9.10#Ex1] || [[Item:Q2893|<math>\int_{0}^{\infty}\AiryAi@{t}\diff{t} = \tfrac{1}{3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\AiryAi@{t}\diff{t} = \tfrac{1}{3}</syntaxhighlight> || <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]
|-
| [https://dlmf.nist.gov/9.10#Ex2 9.10#Ex2] || [[Item:Q2894|<math>\int_{-\infty}^{0}\AiryAi@{t}\diff{t} = \tfrac{2}{3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{-\infty}^{0}\AiryAi@{t}\diff{t} = \tfrac{2}{3}</syntaxhighlight> || <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]
|-
| [https://dlmf.nist.gov/9.10.E12 9.10.E12] || [[Item:Q2895|<math>\int_{-\infty}^{0}\AiryBi@{t}\diff{t} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{-\infty}^{0}\AiryBi@{t}\diff{t} = 0</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{-\infty}^{\infty}e^{pt}\AiryAi@{t}\diff{t} = e^{p^{3}/3}</syntaxhighlight> || <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
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)</syntaxhighlight> || <math></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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)}</syntaxhighlight> || <math>\Re p > 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
Test Values: {p = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br></div></div> || Skipped - Because timed out
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)}</syntaxhighlight> || <math>\Re p > 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
Test Values: {p = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br></div></div> || Skipped - Because timed out
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <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
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <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
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{x}\!\!\int_{0}^{v}\AiryAi@{t}\diff{t}\diff{v} = x\int_{0}^{x}\AiryAi@{t}\diff{t}-\AiryAi'@{x}+\AiryAi'@{0}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{x}\!\!\int_{0}^{v}\AiryBi@{t}\diff{t}\diff{v} = x\int_{0}^{x}\AiryBi@{t}\diff{t}-\AiryBi'@{x}+\AiryBi'@{0}</syntaxhighlight> || <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]
|-
| [https://dlmf.nist.gov/9.11.E1 9.11.E1] || [[Item:Q2908|<math>\deriv[3]{w}{z}-4z\deriv{w}{z}-2w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[3]{w}{z}-4z\deriv{w}{z}-2w = 0</syntaxhighlight> || <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
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
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
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wronskian@{\AiryAi^{2}@{z},\AiryAi@{z}\AiryBi@{z},\AiryBi^{2}@{z}} = 2\pi^{-3}</syntaxhighlight> || <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
Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1529112816e-1-.8621001058e-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[-0.060755306279053636, -0.0079117802669642]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.015291128133821968, -0.08621001051231339]
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/9.11.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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AiryAi^{2}@{x} = \frac{1}{4\pi\sqrt{3}}\int_{0}^{\infty}\BesselJ{0}@{\tfrac{1}{12}t^{3}+xt}t\diff{t}</syntaxhighlight> || <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
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <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
Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.763924327-.1437296879*I
Test Values: {z = 1.5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int\frac{\diff{z}}{\AiryAi^{2}@{z}} = \pi\frac{\AiryBi@{z}}{\AiryAi@{z}}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int\frac{\diff{z}}{\AiryAi@{z}\AiryBi@{z}} = \pi\ln@{\frac{\AiryBi@{z}}{\AiryAi@{z}}}</syntaxhighlight> || <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]]]
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]]]
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/9.11.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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}</syntaxhighlight> || <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]]]
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[GenerateConditions, None]]]
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/9.11.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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}}</syntaxhighlight> || <math>\realpart@@{\alpha} > 0, \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[]
Test Values: {Rule[α, 0.5]}</syntaxhighlight><br></div></div>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{-\infty}^{\infty}\AiryAi^{3}@{t}\diff{t} = \frac{\EulerGamma^{2}@{\frac{1}{3}}}{4\pi^{2}}</syntaxhighlight> || <math></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
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{-\infty}^{\infty}\AiryAi^{2}@{t}\AiryBi@{t}\diff{t} = \frac{\EulerGamma^{2}@{\frac{1}{3}}}{4\sqrt{3}\pi^{2}}</syntaxhighlight> || <math></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
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\AiryAi^{4}@{t}\diff{t} = \frac{\ln@@{3}}{24\pi^{2}}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\frac{t\diff{t}}{\AiryAi'^{2}@{t}+\AiryBi'^{2}@{t}} = \frac{\pi^{2}}{6}</syntaxhighlight> || <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]
|-
| [https://dlmf.nist.gov/9.12.E1 9.12.E1] || [[Item:Q2927|<math>\deriv[2]{w}{z}-zw = \frac{1}{\pi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}-zw = \frac{1}{\pi}</syntaxhighlight> || <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
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
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]
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]
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>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ScorerGi@{z} = \AiryBi@{z}\int_{z}^{\infty}\AiryAi@{t}\diff{t}+\AiryAi@{z}\int_{0}^{z}\AiryBi@{t}\diff{t}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ScorerHi@{z} = \AiryBi@{z}\int_{-\infty}^{z}\AiryAi@{t}\diff{t}-\AiryAi@{z}\int_{-\infty}^{z}\AiryBi@{t}\diff{t}</syntaxhighlight> || <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]
|-
| [https://dlmf.nist.gov/9.12.E6 9.12.E6] || [[Item:Q2934|<math>\ScorerGi@{0} = \tfrac{1}{2}\ScorerHi@{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ScorerGi@{0} = \tfrac{1}{2}\ScorerHi@{0}</syntaxhighlight> || <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]
|-
| [https://dlmf.nist.gov/9.12.E6 9.12.E6] || [[Item:Q2934|<math>\tfrac{1}{2}\ScorerHi@{0} = \tfrac{1}{3}\AiryBi@{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tfrac{1}{2}\ScorerHi@{0} = \tfrac{1}{3}\AiryBi@{0}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tfrac{1}{3}\AiryBi@{0} = {1\Big{/}\!\left(3^{7/6}\EulerGamma@{\tfrac{2}{3}}\right)=0.20497\;55424\ldots,}</syntaxhighlight> || <math></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
|-
| [https://dlmf.nist.gov/9.12.E7 9.12.E7] || [[Item:Q2935|<math>\ScorerGi'@{0} = \tfrac{1}{2}\ScorerHi'@{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ScorerGi'@{0} = \tfrac{1}{2}\ScorerHi'@{0}</syntaxhighlight> || <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$(1) ) )</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[ScorerGi[temp], {temp, 1}]/.temp-> 0) == Divide[1,2]*(D[ScorerHi[temp], {temp, 1}]/.temp-> 0)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
|-
| [https://dlmf.nist.gov/9.12.E7 9.12.E7] || [[Item:Q2935|<math>\tfrac{1}{2}\ScorerHi'@{0} = \tfrac{1}{3}\AiryBi'@{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tfrac{1}{2}\ScorerHi'@{0} = \tfrac{1}{3}\AiryBi'@{0}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(2)*subs( temp=0, diff( AiryBi(temp)*(int(AiryAi(t), t = -infinity .. (temp)))-AiryAi(temp)*(int(AiryBi(t), t = -infinity .. (temp))), temp$(1) ) ) = (1)/(3)*subs( temp=0, diff( AiryBi(temp), temp$(1) ) )</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,2]*(D[ScorerHi[temp], {temp, 1}]/.temp-> 0) == Divide[1,3]*(D[AiryBi[temp], {temp, 1}]/.temp-> 0)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
|-
| [https://dlmf.nist.gov/9.12.E7 9.12.E7] || [[Item:Q2935|<math>\tfrac{1}{3}\AiryBi'@{0} = 1\Big{/}\left(3^{5/6}\EulerGamma@{\tfrac{1}{3}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tfrac{1}{3}\AiryBi'@{0} = 1\Big{/}\left(3^{5/6}\EulerGamma@{\tfrac{1}{3}}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(3)*subs( temp=0, diff( AiryBi(temp), temp$(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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>1\Big{/}\left(3^{5/6}\EulerGamma@{\tfrac{1}{3}}\right) = 0.14942\;94524\ldots</syntaxhighlight> || <math></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]
|-
| [https://dlmf.nist.gov/9.12.E11 9.12.E11] || [[Item:Q2939|<math>\ScorerGi@{z}+\ScorerHi@{z} = \AiryBi@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ScorerGi@{z}+\ScorerHi@{z} = \AiryBi@{z}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}</syntaxhighlight> || <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
Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1024598659-.3465846956*I
Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ScorerGi@{z} = e^{-\pi i/3}\ScorerHi@{ze^{+ 2\pi i/3}}+ i\AiryAi@{z}</syntaxhighlight> || <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
Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1844815903-.2874294645*I
Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ScorerGi@{z} = e^{+\pi i/3}\ScorerHi@{ze^{- 2\pi i/3}}- i\AiryAi@{z}</syntaxhighlight> || <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
Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .590395216e-1-.1022594507*I
Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ScorerHi@{z} = e^{+ 2\pi i/3}\ScorerHi@{ze^{+ 2\pi i/3}}+2e^{-\pi i/6}\AiryAi@{ze^{- 2\pi i/3}}</syntaxhighlight> || <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
Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.4978424366-.3195314878*I
Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ScorerHi@{z} = e^{- 2\pi i/3}\ScorerHi@{ze^{- 2\pi i/3}}+2e^{+\pi i/6}\AiryAi@{ze^{+ 2\pi i/3}}</syntaxhighlight> || <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
Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1771185635+.1022594505*I
Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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!}</syntaxhighlight> || <math></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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff( AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z))), z$(1) ) = ((3)^(- 1/3))/(Pi)* sum(cos((2*k + 1)/(3)*Pi)*GAMMA((k + 2)/(3))*(((3)^(1/3)* z)^(k))/(factorial(k)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[ScorerGi[z], {z, 1}] == Divide[(3)^(- 1/3),Pi]* Sum[Cos[Divide[2*k + 1,3]*Pi]*Gamma[Divide[k + 2,3]]*Divide[((3)^(1/3)* z)^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
|-
| [https://dlmf.nist.gov/9.12.E17 9.12.E17] || [[Item:Q2945|<math>\ScorerHi@{z} = \frac{3^{-2/3}}{\pi}\sum_{k=0}^{\infty}\EulerGamma@{\frac{k+1}{3}}\frac{(3^{1/3}z)^{k}}{k!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ScorerHi@{z} = \frac{3^{-2/3}}{\pi}\sum_{k=0}^{\infty}\EulerGamma@{\frac{k+1}{3}}\frac{(3^{1/3}z)^{k}}{k!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z))) = ((3)^(- 2/3))/(Pi)*sum(GAMMA((k + 1)/(3))*(((3)^(1/3)* z)^(k))/(factorial(k)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ScorerHi[z] == Divide[(3)^(- 2/3),Pi]*Sum[Gamma[Divide[k + 1,3]]*Divide[((3)^(1/3)* z)^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
|-
| [https://dlmf.nist.gov/9.12.E18 9.12.E18] || [[Item:Q2946|<math>\ScorerHi'@{z} = \frac{3^{-1/3}}{\pi}\sum_{k=0}^{\infty}\EulerGamma@{\frac{k+2}{3}}\frac{(3^{1/3}z)^{k}}{k!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ScorerHi'@{z} = \frac{3^{-1/3}}{\pi}\sum_{k=0}^{\infty}\EulerGamma@{\frac{k+2}{3}}\frac{(3^{1/3}z)^{k}}{k!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff( AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z))), z$(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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ScorerGi@{x} = \frac{1}{\pi}\int_{0}^{\infty}\sin@{\tfrac{1}{3}t^{3}+xt}\diff{t}</syntaxhighlight> || <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]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ScorerHi@{z} = \frac{1}{\pi}\int_{0}^{\infty}\exp@{-\tfrac{1}{3}t^{3}+zt}\diff{t}</syntaxhighlight> || <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
Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.510759173-.1408206709*I
Test Values: {z = 1.5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <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
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ScorerHi@{-z} = \frac{4z^{2}}{3^{3/2}\pi^{2}}\int_{0}^{\infty}\frac{\modBesselK{1/3}@{t}}{\zeta^{2}+t^{2}}\diff{t}</syntaxhighlight> || <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
Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .528823090e-1
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]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0.05288230872547964
Test Values: {Rule[z, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <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
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/9.13#Ex7 9.13#Ex7] || [[Item:Q2976|<math>m = n+2</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>m = n+2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">m = n + 2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">m == n + 2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/9.13#Ex8 9.13#Ex8] || [[Item:Q2977|<math>t = (\tfrac{1}{2}m)^{-2/m}z</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>t = (\tfrac{1}{2}m)^{-2/m}z</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">t = ((1)/(2)*m)^(- 2/m)* z</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">t == (Divide[1,2]*m)^(- 2/m)* z</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>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}}</syntaxhighlight> || <math></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
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>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}}</syntaxhighlight> || <math></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
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/9.13#Ex9 9.13#Ex9] || [[Item:Q2985|<math>\alpha = m-2</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha = m-2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha = m - 2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Alpha] == m - 2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/9.13#Ex10 9.13#Ex10] || [[Item:Q2986|<math>x = (m/2)^{2/m}t</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x = (m/2)^{2/m}t</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x = (m/2)^(2/m)* t</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x == (m/2)^(2/m)* t</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>U_{1}(x,\alpha) = \frac{\pi^{1/2}}{2^{(m+2)/(2m)}\EulerGamma@{1/m}}\left(W_{m}(t)+W_{m}(-t)\right)</syntaxhighlight> || <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
|-
| [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>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>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)</syntaxhighlight> || <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
|}
</div>
</div>

Latest revision as of 16:50, 25 May 2021

Notation
9.1 Special Notation
Airy Functions
9.2 Differential Equation
9.3 Graphics
9.4 Maclaurin Series
9.5 Integral Representations
9.6 Relations to Other Functions
9.7 Asymptotic Expansions
9.8 Modulus and Phase
9.9 Zeros
9.10 Integrals
9.11 Products
Related Functions
9.12 Scorer Functions
9.13 Generalized Airy Functions
9.14 Incomplete Airy Functions
Applications
9.15 Mathematical Applications
9.16 Physical Applications
Computation
9.17 Methods of Computation
9.18 Tables
9.19 Approximations
9.20 Software
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