18.7: Difference between revisions

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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/18.7.E1 18.7.E1] || [[Item:Q5569|<math>\ultrasphpoly{\lambda}{n}@{x} = \frac{\Pochhammersym{2\lambda}{n}}{\Pochhammersym{\lambda+\frac{1}{2}}{n}}\JacobipolyP{\lambda-\frac{1}{2}}{\lambda-\frac{1}{2}}{n}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ultrasphpoly{\lambda}{n}@{x} = \frac{\Pochhammersym{2\lambda}{n}}{\Pochhammersym{\lambda+\frac{1}{2}}{n}}\JacobipolyP{\lambda-\frac{1}{2}}{\lambda-\frac{1}{2}}{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GegenbauerC(n, lambda, x) = (pochhammer(2*lambda, n))/(pochhammer(lambda +(1)/(2), n))*JacobiP(n, lambda -(1)/(2), lambda -(1)/(2), x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GegenbauerC[n, \[Lambda], x] == Divide[Pochhammer[2*\[Lambda], n],Pochhammer[\[Lambda]+Divide[1,2], n]]*JacobiP[n, \[Lambda]-Divide[1,2], \[Lambda]-Divide[1,2], x]</syntaxhighlight> || Successful || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [15 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
| [https://dlmf.nist.gov/18.7.E1 18.7.E1] || <math qid="Q5569">\ultrasphpoly{\lambda}{n}@{x} = \frac{\Pochhammersym{2\lambda}{n}}{\Pochhammersym{\lambda+\frac{1}{2}}{n}}\JacobipolyP{\lambda-\frac{1}{2}}{\lambda-\frac{1}{2}}{n}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ultrasphpoly{\lambda}{n}@{x} = \frac{\Pochhammersym{2\lambda}{n}}{\Pochhammersym{\lambda+\frac{1}{2}}{n}}\JacobipolyP{\lambda-\frac{1}{2}}{\lambda-\frac{1}{2}}{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GegenbauerC(n, lambda, x) = (pochhammer(2*lambda, n))/(pochhammer(lambda +(1)/(2), n))*JacobiP(n, lambda -(1)/(2), lambda -(1)/(2), x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GegenbauerC[n, \[Lambda], x] == Divide[Pochhammer[2*\[Lambda], n],Pochhammer[\[Lambda]+Divide[1,2], n]]*JacobiP[n, \[Lambda]-Divide[1,2], \[Lambda]-Divide[1,2], x]</syntaxhighlight> || Successful || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [15 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[λ, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[λ, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[n, 3], Rule[x, 1.5], Rule[λ, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[n, 3], Rule[x, 1.5], Rule[λ, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/18.7.E2 18.7.E2] || [[Item:Q5570|<math>\JacobipolyP{\alpha}{\alpha}{n}@{x} = \frac{\Pochhammersym{\alpha+1}{n}}{\Pochhammersym{2\alpha+1}{n}}\ultrasphpoly{\alpha+\frac{1}{2}}{n}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\JacobipolyP{\alpha}{\alpha}{n}@{x} = \frac{\Pochhammersym{\alpha+1}{n}}{\Pochhammersym{2\alpha+1}{n}}\ultrasphpoly{\alpha+\frac{1}{2}}{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiP(n, alpha, alpha, x) = (pochhammer(alpha + 1, n))/(pochhammer(2*alpha + 1, n))*GegenbauerC(n, alpha +(1)/(2), x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiP[n, \[Alpha], \[Alpha], x] == Divide[Pochhammer[\[Alpha]+ 1, n],Pochhammer[2*\[Alpha]+ 1, n]]*GegenbauerC[n, \[Alpha]+Divide[1,2], x]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 27]
| [https://dlmf.nist.gov/18.7.E2 18.7.E2] || <math qid="Q5570">\JacobipolyP{\alpha}{\alpha}{n}@{x} = \frac{\Pochhammersym{\alpha+1}{n}}{\Pochhammersym{2\alpha+1}{n}}\ultrasphpoly{\alpha+\frac{1}{2}}{n}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\JacobipolyP{\alpha}{\alpha}{n}@{x} = \frac{\Pochhammersym{\alpha+1}{n}}{\Pochhammersym{2\alpha+1}{n}}\ultrasphpoly{\alpha+\frac{1}{2}}{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiP(n, alpha, alpha, x) = (pochhammer(alpha + 1, n))/(pochhammer(2*alpha + 1, n))*GegenbauerC(n, alpha +(1)/(2), x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiP[n, \[Alpha], \[Alpha], x] == Divide[Pochhammer[\[Alpha]+ 1, n],Pochhammer[2*\[Alpha]+ 1, n]]*GegenbauerC[n, \[Alpha]+Divide[1,2], x]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 27]
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| [https://dlmf.nist.gov/18.7.E3 18.7.E3] || [[Item:Q5571|<math>\ChebyshevpolyT{n}@{x} = \ifrac{\JacobipolyP{-\frac{1}{2}}{-\frac{1}{2}}{n}@{x}}{\JacobipolyP{-\frac{1}{2}}{-\frac{1}{2}}{n}@{1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ChebyshevpolyT{n}@{x} = \ifrac{\JacobipolyP{-\frac{1}{2}}{-\frac{1}{2}}{n}@{x}}{\JacobipolyP{-\frac{1}{2}}{-\frac{1}{2}}{n}@{1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>ChebyshevT(n, x) = (JacobiP(n, -(1)/(2), -(1)/(2), x))/(JacobiP(n, -(1)/(2), -(1)/(2), 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ChebyshevT[n, x] == Divide[JacobiP[n, -Divide[1,2], -Divide[1,2], x],JacobiP[n, -Divide[1,2], -Divide[1,2], 1]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
| [https://dlmf.nist.gov/18.7.E3 18.7.E3] || <math qid="Q5571">\ChebyshevpolyT{n}@{x} = \ifrac{\JacobipolyP{-\frac{1}{2}}{-\frac{1}{2}}{n}@{x}}{\JacobipolyP{-\frac{1}{2}}{-\frac{1}{2}}{n}@{1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ChebyshevpolyT{n}@{x} = \ifrac{\JacobipolyP{-\frac{1}{2}}{-\frac{1}{2}}{n}@{x}}{\JacobipolyP{-\frac{1}{2}}{-\frac{1}{2}}{n}@{1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>ChebyshevT(n, x) = (JacobiP(n, -(1)/(2), -(1)/(2), x))/(JacobiP(n, -(1)/(2), -(1)/(2), 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ChebyshevT[n, x] == Divide[JacobiP[n, -Divide[1,2], -Divide[1,2], x],JacobiP[n, -Divide[1,2], -Divide[1,2], 1]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
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| [https://dlmf.nist.gov/18.7.E4 18.7.E4] || [[Item:Q5572|<math>\ChebyshevpolyU{n}@{x} = \ultrasphpoly{1}{n}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ChebyshevpolyU{n}@{x} = \ultrasphpoly{1}{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>ChebyshevU(n, x) = GegenbauerC(n, 1, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ChebyshevU[n, x] == GegenbauerC[n, 1, x]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
| [https://dlmf.nist.gov/18.7.E4 18.7.E4] || <math qid="Q5572">\ChebyshevpolyU{n}@{x} = \ultrasphpoly{1}{n}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ChebyshevpolyU{n}@{x} = \ultrasphpoly{1}{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>ChebyshevU(n, x) = GegenbauerC(n, 1, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ChebyshevU[n, x] == GegenbauerC[n, 1, x]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
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| [https://dlmf.nist.gov/18.7.E4 18.7.E4] || [[Item:Q5572|<math>\ultrasphpoly{1}{n}@{x} = \ifrac{(n+1)\JacobipolyP{\frac{1}{2}}{\frac{1}{2}}{n}@{x}}{\JacobipolyP{\frac{1}{2}}{\frac{1}{2}}{n}@{1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ultrasphpoly{1}{n}@{x} = \ifrac{(n+1)\JacobipolyP{\frac{1}{2}}{\frac{1}{2}}{n}@{x}}{\JacobipolyP{\frac{1}{2}}{\frac{1}{2}}{n}@{1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GegenbauerC(n, 1, x) = ((n + 1)*JacobiP(n, (1)/(2), (1)/(2), x))/(JacobiP(n, (1)/(2), (1)/(2), 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>GegenbauerC[n, 1, x] == Divide[(n + 1)*JacobiP[n, Divide[1,2], Divide[1,2], x],JacobiP[n, Divide[1,2], Divide[1,2], 1]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
| [https://dlmf.nist.gov/18.7.E4 18.7.E4] || <math qid="Q5572">\ultrasphpoly{1}{n}@{x} = \ifrac{(n+1)\JacobipolyP{\frac{1}{2}}{\frac{1}{2}}{n}@{x}}{\JacobipolyP{\frac{1}{2}}{\frac{1}{2}}{n}@{1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ultrasphpoly{1}{n}@{x} = \ifrac{(n+1)\JacobipolyP{\frac{1}{2}}{\frac{1}{2}}{n}@{x}}{\JacobipolyP{\frac{1}{2}}{\frac{1}{2}}{n}@{1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GegenbauerC(n, 1, x) = ((n + 1)*JacobiP(n, (1)/(2), (1)/(2), x))/(JacobiP(n, (1)/(2), (1)/(2), 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>GegenbauerC[n, 1, x] == Divide[(n + 1)*JacobiP[n, Divide[1,2], Divide[1,2], x],JacobiP[n, Divide[1,2], Divide[1,2], 1]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
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| [https://dlmf.nist.gov/18.7.E9 18.7.E9] || [[Item:Q5577|<math>\LegendrepolyP{n}@{x} = \ultrasphpoly{\frac{1}{2}}{n}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\LegendrepolyP{n}@{x} = \ultrasphpoly{\frac{1}{2}}{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LegendreP(n, x) = GegenbauerC(n, (1)/(2), x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>LegendreP[n, x] == GegenbauerC[n, Divide[1,2], x]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
| [https://dlmf.nist.gov/18.7.E9 18.7.E9] || <math qid="Q5577">\LegendrepolyP{n}@{x} = \ultrasphpoly{\frac{1}{2}}{n}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\LegendrepolyP{n}@{x} = \ultrasphpoly{\frac{1}{2}}{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LegendreP(n, x) = GegenbauerC(n, (1)/(2), x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>LegendreP[n, x] == GegenbauerC[n, Divide[1,2], x]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
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| [https://dlmf.nist.gov/18.7.E9 18.7.E9] || [[Item:Q5577|<math>\ultrasphpoly{\frac{1}{2}}{n}@{x} = \JacobipolyP{0}{0}{n}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ultrasphpoly{\frac{1}{2}}{n}@{x} = \JacobipolyP{0}{0}{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GegenbauerC(n, (1)/(2), x) = JacobiP(n, 0, 0, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GegenbauerC[n, Divide[1,2], x] == JacobiP[n, 0, 0, x]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
| [https://dlmf.nist.gov/18.7.E9 18.7.E9] || <math qid="Q5577">\ultrasphpoly{\frac{1}{2}}{n}@{x} = \JacobipolyP{0}{0}{n}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ultrasphpoly{\frac{1}{2}}{n}@{x} = \JacobipolyP{0}{0}{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GegenbauerC(n, (1)/(2), x) = JacobiP(n, 0, 0, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GegenbauerC[n, Divide[1,2], x] == JacobiP[n, 0, 0, x]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
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| [https://dlmf.nist.gov/18.7.E10 18.7.E10] || [[Item:Q5578|<math>\shiftLegendrepolyP{n}@{x} = \LegendrepolyP{n}@{2x-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\shiftLegendrepolyP{n}@{x} = \LegendrepolyP{n}@{2x-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LegendreP(n, 2*(x) - 1) = LegendreP(n, 2*x - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
| [https://dlmf.nist.gov/18.7.E10 18.7.E10] || <math qid="Q5578">\shiftLegendrepolyP{n}@{x} = \LegendrepolyP{n}@{2x-1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\shiftLegendrepolyP{n}@{x} = \LegendrepolyP{n}@{2x-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LegendreP(n, 2*(x) - 1) = LegendreP(n, 2*x - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
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| [https://dlmf.nist.gov/18.7.E13 18.7.E13] || [[Item:Q5581|<math>\frac{\JacobipolyP{\alpha}{\alpha}{2n}@{x}}{\JacobipolyP{\alpha}{\alpha}{2n}@{1}} = \frac{\JacobipolyP{\alpha}{-\frac{1}{2}}{n}@{2x^{2}-1}}{\JacobipolyP{\alpha}{-\frac{1}{2}}{n}@{1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\JacobipolyP{\alpha}{\alpha}{2n}@{x}}{\JacobipolyP{\alpha}{\alpha}{2n}@{1}} = \frac{\JacobipolyP{\alpha}{-\frac{1}{2}}{n}@{2x^{2}-1}}{\JacobipolyP{\alpha}{-\frac{1}{2}}{n}@{1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiP(2*n, alpha, alpha, x))/(JacobiP(2*n, alpha, alpha, 1)) = (JacobiP(n, alpha, -(1)/(2), 2*(x)^(2)- 1))/(JacobiP(n, alpha, -(1)/(2), 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[JacobiP[2*n, \[Alpha], \[Alpha], x],JacobiP[2*n, \[Alpha], \[Alpha], 1]] == Divide[JacobiP[n, \[Alpha], -Divide[1,2], 2*(x)^(2)- 1],JacobiP[n, \[Alpha], -Divide[1,2], 1]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 27] || Successful [Tested: 27]
| [https://dlmf.nist.gov/18.7.E13 18.7.E13] || <math qid="Q5581">\frac{\JacobipolyP{\alpha}{\alpha}{2n}@{x}}{\JacobipolyP{\alpha}{\alpha}{2n}@{1}} = \frac{\JacobipolyP{\alpha}{-\frac{1}{2}}{n}@{2x^{2}-1}}{\JacobipolyP{\alpha}{-\frac{1}{2}}{n}@{1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\JacobipolyP{\alpha}{\alpha}{2n}@{x}}{\JacobipolyP{\alpha}{\alpha}{2n}@{1}} = \frac{\JacobipolyP{\alpha}{-\frac{1}{2}}{n}@{2x^{2}-1}}{\JacobipolyP{\alpha}{-\frac{1}{2}}{n}@{1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiP(2*n, alpha, alpha, x))/(JacobiP(2*n, alpha, alpha, 1)) = (JacobiP(n, alpha, -(1)/(2), 2*(x)^(2)- 1))/(JacobiP(n, alpha, -(1)/(2), 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[JacobiP[2*n, \[Alpha], \[Alpha], x],JacobiP[2*n, \[Alpha], \[Alpha], 1]] == Divide[JacobiP[n, \[Alpha], -Divide[1,2], 2*(x)^(2)- 1],JacobiP[n, \[Alpha], -Divide[1,2], 1]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 27] || Successful [Tested: 27]
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| [https://dlmf.nist.gov/18.7.E14 18.7.E14] || [[Item:Q5582|<math>\frac{\JacobipolyP{\alpha}{\alpha}{2n+1}@{x}}{\JacobipolyP{\alpha}{\alpha}{2n+1}@{1}} = \frac{x\JacobipolyP{\alpha}{\frac{1}{2}}{n}@{2x^{2}-1}}{\JacobipolyP{\alpha}{\frac{1}{2}}{n}@{1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\JacobipolyP{\alpha}{\alpha}{2n+1}@{x}}{\JacobipolyP{\alpha}{\alpha}{2n+1}@{1}} = \frac{x\JacobipolyP{\alpha}{\frac{1}{2}}{n}@{2x^{2}-1}}{\JacobipolyP{\alpha}{\frac{1}{2}}{n}@{1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiP(2*n + 1, alpha, alpha, x))/(JacobiP(2*n + 1, alpha, alpha, 1)) = (x*JacobiP(n, alpha, (1)/(2), 2*(x)^(2)- 1))/(JacobiP(n, alpha, (1)/(2), 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[JacobiP[2*n + 1, \[Alpha], \[Alpha], x],JacobiP[2*n + 1, \[Alpha], \[Alpha], 1]] == Divide[x*JacobiP[n, \[Alpha], Divide[1,2], 2*(x)^(2)- 1],JacobiP[n, \[Alpha], Divide[1,2], 1]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 27] || Successful [Tested: 27]
| [https://dlmf.nist.gov/18.7.E14 18.7.E14] || <math qid="Q5582">\frac{\JacobipolyP{\alpha}{\alpha}{2n+1}@{x}}{\JacobipolyP{\alpha}{\alpha}{2n+1}@{1}} = \frac{x\JacobipolyP{\alpha}{\frac{1}{2}}{n}@{2x^{2}-1}}{\JacobipolyP{\alpha}{\frac{1}{2}}{n}@{1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\JacobipolyP{\alpha}{\alpha}{2n+1}@{x}}{\JacobipolyP{\alpha}{\alpha}{2n+1}@{1}} = \frac{x\JacobipolyP{\alpha}{\frac{1}{2}}{n}@{2x^{2}-1}}{\JacobipolyP{\alpha}{\frac{1}{2}}{n}@{1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiP(2*n + 1, alpha, alpha, x))/(JacobiP(2*n + 1, alpha, alpha, 1)) = (x*JacobiP(n, alpha, (1)/(2), 2*(x)^(2)- 1))/(JacobiP(n, alpha, (1)/(2), 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[JacobiP[2*n + 1, \[Alpha], \[Alpha], x],JacobiP[2*n + 1, \[Alpha], \[Alpha], 1]] == Divide[x*JacobiP[n, \[Alpha], Divide[1,2], 2*(x)^(2)- 1],JacobiP[n, \[Alpha], Divide[1,2], 1]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 27] || Successful [Tested: 27]
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| [https://dlmf.nist.gov/18.7.E15 18.7.E15] || [[Item:Q5583|<math>\ultrasphpoly{\lambda}{2n}@{x} = \frac{\Pochhammersym{\lambda}{n}}{\Pochhammersym{\tfrac{1}{2}}{n}}\JacobipolyP{\lambda-\frac{1}{2}}{-\frac{1}{2}}{n}@{2x^{2}-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ultrasphpoly{\lambda}{2n}@{x} = \frac{\Pochhammersym{\lambda}{n}}{\Pochhammersym{\tfrac{1}{2}}{n}}\JacobipolyP{\lambda-\frac{1}{2}}{-\frac{1}{2}}{n}@{2x^{2}-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GegenbauerC(2*n, lambda, x) = (pochhammer(lambda, n))/(pochhammer((1)/(2), n))*JacobiP(n, lambda -(1)/(2), -(1)/(2), 2*(x)^(2)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GegenbauerC[2*n, \[Lambda], x] == Divide[Pochhammer[\[Lambda], n],Pochhammer[Divide[1,2], n]]*JacobiP[n, \[Lambda]-Divide[1,2], -Divide[1,2], 2*(x)^(2)- 1]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [15 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
| [https://dlmf.nist.gov/18.7.E15 18.7.E15] || <math qid="Q5583">\ultrasphpoly{\lambda}{2n}@{x} = \frac{\Pochhammersym{\lambda}{n}}{\Pochhammersym{\tfrac{1}{2}}{n}}\JacobipolyP{\lambda-\frac{1}{2}}{-\frac{1}{2}}{n}@{2x^{2}-1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ultrasphpoly{\lambda}{2n}@{x} = \frac{\Pochhammersym{\lambda}{n}}{\Pochhammersym{\tfrac{1}{2}}{n}}\JacobipolyP{\lambda-\frac{1}{2}}{-\frac{1}{2}}{n}@{2x^{2}-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GegenbauerC(2*n, lambda, x) = (pochhammer(lambda, n))/(pochhammer((1)/(2), n))*JacobiP(n, lambda -(1)/(2), -(1)/(2), 2*(x)^(2)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GegenbauerC[2*n, \[Lambda], x] == Divide[Pochhammer[\[Lambda], n],Pochhammer[Divide[1,2], n]]*JacobiP[n, \[Lambda]-Divide[1,2], -Divide[1,2], 2*(x)^(2)- 1]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [15 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
Test Values: {lambda = -3/2, x = 3/2, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(undefined)+Float(undefined)*I
Test Values: {lambda = -3/2, x = 3/2, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(undefined)+Float(undefined)*I
Test Values: {lambda = -3/2, x = 3/2, n = 3}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 90]
Test Values: {lambda = -3/2, x = 3/2, n = 3}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 90]
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| [https://dlmf.nist.gov/18.7.E16 18.7.E16] || [[Item:Q5584|<math>\ultrasphpoly{\lambda}{2n+1}@{x} = \frac{\Pochhammersym{\lambda}{n+1}}{\Pochhammersym{\frac{1}{2}}{n+1}}x\JacobipolyP{\lambda-\frac{1}{2}}{\frac{1}{2}}{n}@{2x^{2}-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ultrasphpoly{\lambda}{2n+1}@{x} = \frac{\Pochhammersym{\lambda}{n+1}}{\Pochhammersym{\frac{1}{2}}{n+1}}x\JacobipolyP{\lambda-\frac{1}{2}}{\frac{1}{2}}{n}@{2x^{2}-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GegenbauerC(2*n + 1, lambda, x) = (pochhammer(lambda, n + 1))/(pochhammer((1)/(2), n + 1))*x*JacobiP(n, lambda -(1)/(2), (1)/(2), 2*(x)^(2)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GegenbauerC[2*n + 1, \[Lambda], x] == Divide[Pochhammer[\[Lambda], n + 1],Pochhammer[Divide[1,2], n + 1]]*x*JacobiP[n, \[Lambda]-Divide[1,2], Divide[1,2], 2*(x)^(2)- 1]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [15 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
| [https://dlmf.nist.gov/18.7.E16 18.7.E16] || <math qid="Q5584">\ultrasphpoly{\lambda}{2n+1}@{x} = \frac{\Pochhammersym{\lambda}{n+1}}{\Pochhammersym{\frac{1}{2}}{n+1}}x\JacobipolyP{\lambda-\frac{1}{2}}{\frac{1}{2}}{n}@{2x^{2}-1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ultrasphpoly{\lambda}{2n+1}@{x} = \frac{\Pochhammersym{\lambda}{n+1}}{\Pochhammersym{\frac{1}{2}}{n+1}}x\JacobipolyP{\lambda-\frac{1}{2}}{\frac{1}{2}}{n}@{2x^{2}-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GegenbauerC(2*n + 1, lambda, x) = (pochhammer(lambda, n + 1))/(pochhammer((1)/(2), n + 1))*x*JacobiP(n, lambda -(1)/(2), (1)/(2), 2*(x)^(2)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GegenbauerC[2*n + 1, \[Lambda], x] == Divide[Pochhammer[\[Lambda], n + 1],Pochhammer[Divide[1,2], n + 1]]*x*JacobiP[n, \[Lambda]-Divide[1,2], Divide[1,2], 2*(x)^(2)- 1]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [15 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
Test Values: {lambda = -3/2, x = 3/2, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(undefined)+Float(undefined)*I
Test Values: {lambda = -3/2, x = 3/2, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(undefined)+Float(undefined)*I
Test Values: {lambda = -3/2, x = 3/2, n = 3}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 90]
Test Values: {lambda = -3/2, x = 3/2, n = 3}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 90]
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| [https://dlmf.nist.gov/18.7.E19 18.7.E19] || [[Item:Q5587|<math>\HermitepolyH{2n}@{x} = (-1)^{n}2^{2n}n!\LaguerrepolyL[-\frac{1}{2}]{n}@{x^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\HermitepolyH{2n}@{x} = (-1)^{n}2^{2n}n!\LaguerrepolyL[-\frac{1}{2}]{n}@{x^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>HermiteH(2*n, x) = (- 1)^(n)* (2)^(2*n)* factorial(n)*LaguerreL(n, -(1)/(2), (x)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>HermiteH[2*n, x] == (- 1)^(n)* (2)^(2*n)* (n)!*LaguerreL[n, -Divide[1,2], (x)^(2)]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 9]
| [https://dlmf.nist.gov/18.7.E19 18.7.E19] || <math qid="Q5587">\HermitepolyH{2n}@{x} = (-1)^{n}2^{2n}n!\LaguerrepolyL[-\frac{1}{2}]{n}@{x^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\HermitepolyH{2n}@{x} = (-1)^{n}2^{2n}n!\LaguerrepolyL[-\frac{1}{2}]{n}@{x^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>HermiteH(2*n, x) = (- 1)^(n)* (2)^(2*n)* factorial(n)*LaguerreL(n, -(1)/(2), (x)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>HermiteH[2*n, x] == (- 1)^(n)* (2)^(2*n)* (n)!*LaguerreL[n, -Divide[1,2], (x)^(2)]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 9]
|-  
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| [https://dlmf.nist.gov/18.7.E20 18.7.E20] || [[Item:Q5588|<math>\HermitepolyH{2n+1}@{x} = (-1)^{n}2^{2n+1}n!\,x\LaguerrepolyL[\frac{1}{2}]{n}@{x^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\HermitepolyH{2n+1}@{x} = (-1)^{n}2^{2n+1}n!\,x\LaguerrepolyL[\frac{1}{2}]{n}@{x^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>HermiteH(2*n + 1, x) = (- 1)^(n)* (2)^(2*n + 1)* factorial(n)*x*LaguerreL(n, (1)/(2), (x)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>HermiteH[2*n + 1, x] == (- 1)^(n)* (2)^(2*n + 1)* (n)!*x*LaguerreL[n, Divide[1,2], (x)^(2)]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 9]
| [https://dlmf.nist.gov/18.7.E20 18.7.E20] || <math qid="Q5588">\HermitepolyH{2n+1}@{x} = (-1)^{n}2^{2n+1}n!\,x\LaguerrepolyL[\frac{1}{2}]{n}@{x^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\HermitepolyH{2n+1}@{x} = (-1)^{n}2^{2n+1}n!\,x\LaguerrepolyL[\frac{1}{2}]{n}@{x^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>HermiteH(2*n + 1, x) = (- 1)^(n)* (2)^(2*n + 1)* factorial(n)*x*LaguerreL(n, (1)/(2), (x)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>HermiteH[2*n + 1, x] == (- 1)^(n)* (2)^(2*n + 1)* (n)!*x*LaguerreL[n, Divide[1,2], (x)^(2)]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 9]
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| [https://dlmf.nist.gov/18.7.E21 18.7.E21] || [[Item:Q5589|<math>\lim_{\beta\to\infty}\JacobipolyP{\alpha}{\beta}{n}@{1-(\ifrac{2x}{\beta})} = \LaguerrepolyL[\alpha]{n}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\beta\to\infty}\JacobipolyP{\alpha}{\beta}{n}@{1-(\ifrac{2x}{\beta})} = \LaguerrepolyL[\alpha]{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit(JacobiP(n, alpha, beta, 1 -((2*x)/(beta))), beta = infinity) = LaguerreL(n, alpha, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[JacobiP[n, \[Alpha], \[Beta], 1 -(Divide[2*x,\[Beta]])], \[Beta] -> Infinity, GenerateConditions->None] == LaguerreL[n, \[Alpha], x]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 27]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
| [https://dlmf.nist.gov/18.7.E21 18.7.E21] || <math qid="Q5589">\lim_{\beta\to\infty}\JacobipolyP{\alpha}{\beta}{n}@{1-(\ifrac{2x}{\beta})} = \LaguerrepolyL[\alpha]{n}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\beta\to\infty}\JacobipolyP{\alpha}{\beta}{n}@{1-(\ifrac{2x}{\beta})} = \LaguerrepolyL[\alpha]{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit(JacobiP(n, alpha, beta, 1 -((2*x)/(beta))), beta = infinity) = LaguerreL(n, alpha, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[JacobiP[n, \[Alpha], \[Beta], 1 -(Divide[2*x,\[Beta]])], \[Beta] -> Infinity, GenerateConditions->None] == LaguerreL[n, \[Alpha], x]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 27]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[α, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[α, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[α, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[α, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/18.7.E22 18.7.E22] || [[Item:Q5590|<math>\lim_{\alpha\to\infty}\JacobipolyP{\alpha}{\beta}{n}@{(2x/\alpha)-1} = (-1)^{n}\LaguerrepolyL[\beta]{n}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\alpha\to\infty}\JacobipolyP{\alpha}{\beta}{n}@{(2x/\alpha)-1} = (-1)^{n}\LaguerrepolyL[\beta]{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit(JacobiP(n, alpha, beta, (2*x/alpha)- 1), alpha = infinity) = (- 1)^(n)* LaguerreL(n, beta, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[JacobiP[n, \[Alpha], \[Beta], (2*x/\[Alpha])- 1], \[Alpha] -> Infinity, GenerateConditions->None] == (- 1)^(n)* LaguerreL[n, \[Beta], x]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 27]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
| [https://dlmf.nist.gov/18.7.E22 18.7.E22] || <math qid="Q5590">\lim_{\alpha\to\infty}\JacobipolyP{\alpha}{\beta}{n}@{(2x/\alpha)-1} = (-1)^{n}\LaguerrepolyL[\beta]{n}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\alpha\to\infty}\JacobipolyP{\alpha}{\beta}{n}@{(2x/\alpha)-1} = (-1)^{n}\LaguerrepolyL[\beta]{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit(JacobiP(n, alpha, beta, (2*x/alpha)- 1), alpha = infinity) = (- 1)^(n)* LaguerreL(n, beta, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[JacobiP[n, \[Alpha], \[Beta], (2*x/\[Alpha])- 1], \[Alpha] -> Infinity, GenerateConditions->None] == (- 1)^(n)* LaguerreL[n, \[Beta], x]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 27]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[β, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[β, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[β, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[β, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/18.7.E23 18.7.E23] || [[Item:Q5591|<math>\lim_{\alpha\to\infty}\alpha^{-\frac{1}{2}n}\JacobipolyP{\alpha}{\alpha}{n}@{\alpha^{-\frac{1}{2}}x} = \frac{\HermitepolyH{n}@{x}}{2^{n}n!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\alpha\to\infty}\alpha^{-\frac{1}{2}n}\JacobipolyP{\alpha}{\alpha}{n}@{\alpha^{-\frac{1}{2}}x} = \frac{\HermitepolyH{n}@{x}}{2^{n}n!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((alpha)^(-(1)/(2)*n)* JacobiP(n, alpha, alpha, (alpha)^(-(1)/(2))* x), alpha = infinity) = (HermiteH(n, x))/((2)^(n)* factorial(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[\[Alpha]^(-Divide[1,2]*n)* JacobiP[n, \[Alpha], \[Alpha], \[Alpha]^(-Divide[1,2])* x], \[Alpha] -> Infinity, GenerateConditions->None] == Divide[HermiteH[n, x],(2)^(n)* (n)!]</syntaxhighlight> || Failure || Aborted || Error || Successful [Tested: 9]
| [https://dlmf.nist.gov/18.7.E23 18.7.E23] || <math qid="Q5591">\lim_{\alpha\to\infty}\alpha^{-\frac{1}{2}n}\JacobipolyP{\alpha}{\alpha}{n}@{\alpha^{-\frac{1}{2}}x} = \frac{\HermitepolyH{n}@{x}}{2^{n}n!}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\alpha\to\infty}\alpha^{-\frac{1}{2}n}\JacobipolyP{\alpha}{\alpha}{n}@{\alpha^{-\frac{1}{2}}x} = \frac{\HermitepolyH{n}@{x}}{2^{n}n!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((alpha)^(-(1)/(2)*n)* JacobiP(n, alpha, alpha, (alpha)^(-(1)/(2))* x), alpha = infinity) = (HermiteH(n, x))/((2)^(n)* factorial(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[\[Alpha]^(-Divide[1,2]*n)* JacobiP[n, \[Alpha], \[Alpha], \[Alpha]^(-Divide[1,2])* x], \[Alpha] -> Infinity, GenerateConditions->None] == Divide[HermiteH[n, x],(2)^(n)* (n)!]</syntaxhighlight> || Failure || Aborted || Error || Successful [Tested: 9]
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| [https://dlmf.nist.gov/18.7.E24 18.7.E24] || [[Item:Q5592|<math>\lim_{\lambda\to\infty}\lambda^{-\frac{1}{2}n}\ultrasphpoly{\lambda}{n}@{\lambda^{-\frac{1}{2}}x} = \frac{\HermitepolyH{n}@{x}}{n!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\lambda\to\infty}\lambda^{-\frac{1}{2}n}\ultrasphpoly{\lambda}{n}@{\lambda^{-\frac{1}{2}}x} = \frac{\HermitepolyH{n}@{x}}{n!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((lambda)^(-(1)/(2)*n)* GegenbauerC(n, lambda, (lambda)^(-(1)/(2))* x), lambda = infinity) = (HermiteH(n, x))/(factorial(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[\[Lambda]^(-Divide[1,2]*n)* GegenbauerC[n, \[Lambda], \[Lambda]^(-Divide[1,2])* x], \[Lambda] -> Infinity, GenerateConditions->None] == Divide[HermiteH[n, x],(n)!]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 9] || Successful [Tested: 9]
| [https://dlmf.nist.gov/18.7.E24 18.7.E24] || <math qid="Q5592">\lim_{\lambda\to\infty}\lambda^{-\frac{1}{2}n}\ultrasphpoly{\lambda}{n}@{\lambda^{-\frac{1}{2}}x} = \frac{\HermitepolyH{n}@{x}}{n!}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\lambda\to\infty}\lambda^{-\frac{1}{2}n}\ultrasphpoly{\lambda}{n}@{\lambda^{-\frac{1}{2}}x} = \frac{\HermitepolyH{n}@{x}}{n!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((lambda)^(-(1)/(2)*n)* GegenbauerC(n, lambda, (lambda)^(-(1)/(2))* x), lambda = infinity) = (HermiteH(n, x))/(factorial(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[\[Lambda]^(-Divide[1,2]*n)* GegenbauerC[n, \[Lambda], \[Lambda]^(-Divide[1,2])* x], \[Lambda] -> Infinity, GenerateConditions->None] == Divide[HermiteH[n, x],(n)!]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 9] || Successful [Tested: 9]
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| [https://dlmf.nist.gov/18.7.E25 18.7.E25] || [[Item:Q5593|<math>\lim_{\lambda\to 0}\frac{1}{\lambda}\ultrasphpoly{\lambda}{n}@{x} = \frac{2}{n}\ChebyshevpolyT{n}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\lambda\to 0}\frac{1}{\lambda}\ultrasphpoly{\lambda}{n}@{x} = \frac{2}{n}\ChebyshevpolyT{n}@{x}</syntaxhighlight> || <math>n \geq 1</math> || <syntaxhighlight lang=mathematica>limit((1)/(lambda)*GegenbauerC(n, lambda, x), lambda = 0) = (2)/(n)*ChebyshevT(n, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[1,\[Lambda]]*GegenbauerC[n, \[Lambda], x], \[Lambda] -> 0, GenerateConditions->None] == Divide[2,n]*ChebyshevT[n, x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
| [https://dlmf.nist.gov/18.7.E25 18.7.E25] || <math qid="Q5593">\lim_{\lambda\to 0}\frac{1}{\lambda}\ultrasphpoly{\lambda}{n}@{x} = \frac{2}{n}\ChebyshevpolyT{n}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\lambda\to 0}\frac{1}{\lambda}\ultrasphpoly{\lambda}{n}@{x} = \frac{2}{n}\ChebyshevpolyT{n}@{x}</syntaxhighlight> || <math>n \geq 1</math> || <syntaxhighlight lang=mathematica>limit((1)/(lambda)*GegenbauerC(n, lambda, x), lambda = 0) = (2)/(n)*ChebyshevT(n, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[1,\[Lambda]]*GegenbauerC[n, \[Lambda], x], \[Lambda] -> 0, GenerateConditions->None] == Divide[2,n]*ChebyshevT[n, x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
|-  
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| [https://dlmf.nist.gov/18.7.E26 18.7.E26] || [[Item:Q5594|<math>\lim_{\alpha\to\infty}\left(\frac{2}{\alpha}\right)^{\frac{1}{2}n}\LaguerrepolyL[\alpha]{n}@{(2\alpha)^{\frac{1}{2}}x+\alpha} = \frac{(-1)^{n}}{n!}\HermitepolyH{n}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\alpha\to\infty}\left(\frac{2}{\alpha}\right)^{\frac{1}{2}n}\LaguerrepolyL[\alpha]{n}@{(2\alpha)^{\frac{1}{2}}x+\alpha} = \frac{(-1)^{n}}{n!}\HermitepolyH{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit(((2)/(alpha))^((1)/(2)*n)* LaguerreL(n, alpha, (2*alpha)^((1)/(2))* x + alpha), alpha = infinity) = ((- 1)^(n))/(factorial(n))*HermiteH(n, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[(Divide[2,\[Alpha]])^(Divide[1,2]*n)* LaguerreL[n, \[Alpha], (2*\[Alpha])^(Divide[1,2])* x + \[Alpha]], \[Alpha] -> Infinity, GenerateConditions->None] == Divide[(- 1)^(n),(n)!]*HermiteH[n, x]</syntaxhighlight> || Missing Macro Error || Aborted || - || Successful [Tested: 9]
| [https://dlmf.nist.gov/18.7.E26 18.7.E26] || <math qid="Q5594">\lim_{\alpha\to\infty}\left(\frac{2}{\alpha}\right)^{\frac{1}{2}n}\LaguerrepolyL[\alpha]{n}@{(2\alpha)^{\frac{1}{2}}x+\alpha} = \frac{(-1)^{n}}{n!}\HermitepolyH{n}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\alpha\to\infty}\left(\frac{2}{\alpha}\right)^{\frac{1}{2}n}\LaguerrepolyL[\alpha]{n}@{(2\alpha)^{\frac{1}{2}}x+\alpha} = \frac{(-1)^{n}}{n!}\HermitepolyH{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit(((2)/(alpha))^((1)/(2)*n)* LaguerreL(n, alpha, (2*alpha)^((1)/(2))* x + alpha), alpha = infinity) = ((- 1)^(n))/(factorial(n))*HermiteH(n, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[(Divide[2,\[Alpha]])^(Divide[1,2]*n)* LaguerreL[n, \[Alpha], (2*\[Alpha])^(Divide[1,2])* x + \[Alpha]], \[Alpha] -> Infinity, GenerateConditions->None] == Divide[(- 1)^(n),(n)!]*HermiteH[n, x]</syntaxhighlight> || Missing Macro Error || Aborted || - || Successful [Tested: 9]
|}
|}
</div>
</div>

Latest revision as of 12:44, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple
Symbolic
Mathematica
Numeric
Maple
Numeric
Mathematica
18.7.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ultrasphpoly{\lambda}{n}@{x} = \frac{\Pochhammersym{2\lambda}{n}}{\Pochhammersym{\lambda+\frac{1}{2}}{n}}\JacobipolyP{\lambda-\frac{1}{2}}{\lambda-\frac{1}{2}}{n}@{x}}
\ultrasphpoly{\lambda}{n}@{x} = \frac{\Pochhammersym{2\lambda}{n}}{\Pochhammersym{\lambda+\frac{1}{2}}{n}}\JacobipolyP{\lambda-\frac{1}{2}}{\lambda-\frac{1}{2}}{n}@{x}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
GegenbauerC(n, lambda, x) = (pochhammer(2*lambda, n))/(pochhammer(lambda +(1)/(2), n))*JacobiP(n, lambda -(1)/(2), lambda -(1)/(2), x)
GegenbauerC[n, \[Lambda], x] == Divide[Pochhammer[2*\[Lambda], n],Pochhammer[\[Lambda]+Divide[1,2], n]]*JacobiP[n, \[Lambda]-Divide[1,2], \[Lambda]-Divide[1,2], x]
Successful Successful -
Failed [15 / 90]
Result: Indeterminate
Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[λ, -1.5]}

Result: Indeterminate
Test Values: {Rule[n, 3], Rule[x, 1.5], Rule[λ, -1.5]}

... skip entries to safe data
18.7.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \JacobipolyP{\alpha}{\alpha}{n}@{x} = \frac{\Pochhammersym{\alpha+1}{n}}{\Pochhammersym{2\alpha+1}{n}}\ultrasphpoly{\alpha+\frac{1}{2}}{n}@{x}}
\JacobipolyP{\alpha}{\alpha}{n}@{x} = \frac{\Pochhammersym{\alpha+1}{n}}{\Pochhammersym{2\alpha+1}{n}}\ultrasphpoly{\alpha+\frac{1}{2}}{n}@{x}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
JacobiP(n, alpha, alpha, x) = (pochhammer(alpha + 1, n))/(pochhammer(2*alpha + 1, n))*GegenbauerC(n, alpha +(1)/(2), x)
JacobiP[n, \[Alpha], \[Alpha], x] == Divide[Pochhammer[\[Alpha]+ 1, n],Pochhammer[2*\[Alpha]+ 1, n]]*GegenbauerC[n, \[Alpha]+Divide[1,2], x]
Successful Successful - Successful [Tested: 27]
18.7.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyT{n}@{x} = \ifrac{\JacobipolyP{-\frac{1}{2}}{-\frac{1}{2}}{n}@{x}}{\JacobipolyP{-\frac{1}{2}}{-\frac{1}{2}}{n}@{1}}}
\ChebyshevpolyT{n}@{x} = \ifrac{\JacobipolyP{-\frac{1}{2}}{-\frac{1}{2}}{n}@{x}}{\JacobipolyP{-\frac{1}{2}}{-\frac{1}{2}}{n}@{1}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
ChebyshevT(n, x) = (JacobiP(n, -(1)/(2), -(1)/(2), x))/(JacobiP(n, -(1)/(2), -(1)/(2), 1))
ChebyshevT[n, x] == Divide[JacobiP[n, -Divide[1,2], -Divide[1,2], x],JacobiP[n, -Divide[1,2], -Divide[1,2], 1]]
Successful Successful - Successful [Tested: 9]
18.7.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyU{n}@{x} = \ultrasphpoly{1}{n}@{x}}
\ChebyshevpolyU{n}@{x} = \ultrasphpoly{1}{n}@{x}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
ChebyshevU(n, x) = GegenbauerC(n, 1, x)
ChebyshevU[n, x] == GegenbauerC[n, 1, x]
Successful Successful - Successful [Tested: 9]
18.7.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ultrasphpoly{1}{n}@{x} = \ifrac{(n+1)\JacobipolyP{\frac{1}{2}}{\frac{1}{2}}{n}@{x}}{\JacobipolyP{\frac{1}{2}}{\frac{1}{2}}{n}@{1}}}
\ultrasphpoly{1}{n}@{x} = \ifrac{(n+1)\JacobipolyP{\frac{1}{2}}{\frac{1}{2}}{n}@{x}}{\JacobipolyP{\frac{1}{2}}{\frac{1}{2}}{n}@{1}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
GegenbauerC(n, 1, x) = ((n + 1)*JacobiP(n, (1)/(2), (1)/(2), x))/(JacobiP(n, (1)/(2), (1)/(2), 1))
GegenbauerC[n, 1, x] == Divide[(n + 1)*JacobiP[n, Divide[1,2], Divide[1,2], x],JacobiP[n, Divide[1,2], Divide[1,2], 1]]
Successful Successful - Successful [Tested: 9]
18.7.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LegendrepolyP{n}@{x} = \ultrasphpoly{\frac{1}{2}}{n}@{x}}
\LegendrepolyP{n}@{x} = \ultrasphpoly{\frac{1}{2}}{n}@{x}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
LegendreP(n, x) = GegenbauerC(n, (1)/(2), x)
LegendreP[n, x] == GegenbauerC[n, Divide[1,2], x]
Successful Successful - Successful [Tested: 9]
18.7.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ultrasphpoly{\frac{1}{2}}{n}@{x} = \JacobipolyP{0}{0}{n}@{x}}
\ultrasphpoly{\frac{1}{2}}{n}@{x} = \JacobipolyP{0}{0}{n}@{x}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
GegenbauerC(n, (1)/(2), x) = JacobiP(n, 0, 0, x)
GegenbauerC[n, Divide[1,2], x] == JacobiP[n, 0, 0, x]
Successful Successful - Successful [Tested: 9]
18.7.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \shiftLegendrepolyP{n}@{x} = \LegendrepolyP{n}@{2x-1}}
\shiftLegendrepolyP{n}@{x} = \LegendrepolyP{n}@{2x-1}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
LegendreP(n, 2*(x) - 1) = LegendreP(n, 2*x - 1)
Error
Successful Missing Macro Error - -
18.7.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\JacobipolyP{\alpha}{\alpha}{2n}@{x}}{\JacobipolyP{\alpha}{\alpha}{2n}@{1}} = \frac{\JacobipolyP{\alpha}{-\frac{1}{2}}{n}@{2x^{2}-1}}{\JacobipolyP{\alpha}{-\frac{1}{2}}{n}@{1}}}
\frac{\JacobipolyP{\alpha}{\alpha}{2n}@{x}}{\JacobipolyP{\alpha}{\alpha}{2n}@{1}} = \frac{\JacobipolyP{\alpha}{-\frac{1}{2}}{n}@{2x^{2}-1}}{\JacobipolyP{\alpha}{-\frac{1}{2}}{n}@{1}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
(JacobiP(2*n, alpha, alpha, x))/(JacobiP(2*n, alpha, alpha, 1)) = (JacobiP(n, alpha, -(1)/(2), 2*(x)^(2)- 1))/(JacobiP(n, alpha, -(1)/(2), 1))
Divide[JacobiP[2*n, \[Alpha], \[Alpha], x],JacobiP[2*n, \[Alpha], \[Alpha], 1]] == Divide[JacobiP[n, \[Alpha], -Divide[1,2], 2*(x)^(2)- 1],JacobiP[n, \[Alpha], -Divide[1,2], 1]]
Failure Failure Successful [Tested: 27] Successful [Tested: 27]
18.7.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\JacobipolyP{\alpha}{\alpha}{2n+1}@{x}}{\JacobipolyP{\alpha}{\alpha}{2n+1}@{1}} = \frac{x\JacobipolyP{\alpha}{\frac{1}{2}}{n}@{2x^{2}-1}}{\JacobipolyP{\alpha}{\frac{1}{2}}{n}@{1}}}
\frac{\JacobipolyP{\alpha}{\alpha}{2n+1}@{x}}{\JacobipolyP{\alpha}{\alpha}{2n+1}@{1}} = \frac{x\JacobipolyP{\alpha}{\frac{1}{2}}{n}@{2x^{2}-1}}{\JacobipolyP{\alpha}{\frac{1}{2}}{n}@{1}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
(JacobiP(2*n + 1, alpha, alpha, x))/(JacobiP(2*n + 1, alpha, alpha, 1)) = (x*JacobiP(n, alpha, (1)/(2), 2*(x)^(2)- 1))/(JacobiP(n, alpha, (1)/(2), 1))
Divide[JacobiP[2*n + 1, \[Alpha], \[Alpha], x],JacobiP[2*n + 1, \[Alpha], \[Alpha], 1]] == Divide[x*JacobiP[n, \[Alpha], Divide[1,2], 2*(x)^(2)- 1],JacobiP[n, \[Alpha], Divide[1,2], 1]]
Failure Failure Successful [Tested: 27] Successful [Tested: 27]
18.7.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ultrasphpoly{\lambda}{2n}@{x} = \frac{\Pochhammersym{\lambda}{n}}{\Pochhammersym{\tfrac{1}{2}}{n}}\JacobipolyP{\lambda-\frac{1}{2}}{-\frac{1}{2}}{n}@{2x^{2}-1}}
\ultrasphpoly{\lambda}{2n}@{x} = \frac{\Pochhammersym{\lambda}{n}}{\Pochhammersym{\tfrac{1}{2}}{n}}\JacobipolyP{\lambda-\frac{1}{2}}{-\frac{1}{2}}{n}@{2x^{2}-1}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
GegenbauerC(2*n, lambda, x) = (pochhammer(lambda, n))/(pochhammer((1)/(2), n))*JacobiP(n, lambda -(1)/(2), -(1)/(2), 2*(x)^(2)- 1)
GegenbauerC[2*n, \[Lambda], x] == Divide[Pochhammer[\[Lambda], n],Pochhammer[Divide[1,2], n]]*JacobiP[n, \[Lambda]-Divide[1,2], -Divide[1,2], 2*(x)^(2)- 1]
Failure Failure
Failed [15 / 90]
Result: Float(infinity)+Float(infinity)*I
Test Values: {lambda = -3/2, x = 3/2, n = 2}

Result: Float(undefined)+Float(undefined)*I
Test Values: {lambda = -3/2, x = 3/2, n = 3}

... skip entries to safe data
Successful [Tested: 90]
18.7.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ultrasphpoly{\lambda}{2n+1}@{x} = \frac{\Pochhammersym{\lambda}{n+1}}{\Pochhammersym{\frac{1}{2}}{n+1}}x\JacobipolyP{\lambda-\frac{1}{2}}{\frac{1}{2}}{n}@{2x^{2}-1}}
\ultrasphpoly{\lambda}{2n+1}@{x} = \frac{\Pochhammersym{\lambda}{n+1}}{\Pochhammersym{\frac{1}{2}}{n+1}}x\JacobipolyP{\lambda-\frac{1}{2}}{\frac{1}{2}}{n}@{2x^{2}-1}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
GegenbauerC(2*n + 1, lambda, x) = (pochhammer(lambda, n + 1))/(pochhammer((1)/(2), n + 1))*x*JacobiP(n, lambda -(1)/(2), (1)/(2), 2*(x)^(2)- 1)
GegenbauerC[2*n + 1, \[Lambda], x] == Divide[Pochhammer[\[Lambda], n + 1],Pochhammer[Divide[1,2], n + 1]]*x*JacobiP[n, \[Lambda]-Divide[1,2], Divide[1,2], 2*(x)^(2)- 1]
Failure Failure
Failed [15 / 90]
Result: Float(infinity)+Float(infinity)*I
Test Values: {lambda = -3/2, x = 3/2, n = 2}

Result: Float(undefined)+Float(undefined)*I
Test Values: {lambda = -3/2, x = 3/2, n = 3}

... skip entries to safe data
Successful [Tested: 90]
18.7.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HermitepolyH{2n}@{x} = (-1)^{n}2^{2n}n!\LaguerrepolyL[-\frac{1}{2}]{n}@{x^{2}}}
\HermitepolyH{2n}@{x} = (-1)^{n}2^{2n}n!\LaguerrepolyL[-\frac{1}{2}]{n}@{x^{2}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
HermiteH(2*n, x) = (- 1)^(n)* (2)^(2*n)* factorial(n)*LaguerreL(n, -(1)/(2), (x)^(2))
HermiteH[2*n, x] == (- 1)^(n)* (2)^(2*n)* (n)!*LaguerreL[n, -Divide[1,2], (x)^(2)]
Missing Macro Error Failure - Successful [Tested: 9]
18.7.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HermitepolyH{2n+1}@{x} = (-1)^{n}2^{2n+1}n!\,x\LaguerrepolyL[\frac{1}{2}]{n}@{x^{2}}}
\HermitepolyH{2n+1}@{x} = (-1)^{n}2^{2n+1}n!\,x\LaguerrepolyL[\frac{1}{2}]{n}@{x^{2}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
HermiteH(2*n + 1, x) = (- 1)^(n)* (2)^(2*n + 1)* factorial(n)*x*LaguerreL(n, (1)/(2), (x)^(2))
HermiteH[2*n + 1, x] == (- 1)^(n)* (2)^(2*n + 1)* (n)!*x*LaguerreL[n, Divide[1,2], (x)^(2)]
Missing Macro Error Failure - Successful [Tested: 9]
18.7.E21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{\beta\to\infty}\JacobipolyP{\alpha}{\beta}{n}@{1-(\ifrac{2x}{\beta})} = \LaguerrepolyL[\alpha]{n}@{x}}
\lim_{\beta\to\infty}\JacobipolyP{\alpha}{\beta}{n}@{1-(\ifrac{2x}{\beta})} = \LaguerrepolyL[\alpha]{n}@{x}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
limit(JacobiP(n, alpha, beta, 1 -((2*x)/(beta))), beta = infinity) = LaguerreL(n, alpha, x)
Limit[JacobiP[n, \[Alpha], \[Beta], 1 -(Divide[2*x,\[Beta]])], \[Beta] -> Infinity, GenerateConditions->None] == LaguerreL[n, \[Alpha], x]
Missing Macro Error Failure -
Failed [27 / 27]
Result: Indeterminate
Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[α, 1.5]}

Result: Indeterminate
Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[α, 1.5]}

... skip entries to safe data
18.7.E22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{\alpha\to\infty}\JacobipolyP{\alpha}{\beta}{n}@{(2x/\alpha)-1} = (-1)^{n}\LaguerrepolyL[\beta]{n}@{x}}
\lim_{\alpha\to\infty}\JacobipolyP{\alpha}{\beta}{n}@{(2x/\alpha)-1} = (-1)^{n}\LaguerrepolyL[\beta]{n}@{x}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
limit(JacobiP(n, alpha, beta, (2*x/alpha)- 1), alpha = infinity) = (- 1)^(n)* LaguerreL(n, beta, x)
Limit[JacobiP[n, \[Alpha], \[Beta], (2*x/\[Alpha])- 1], \[Alpha] -> Infinity, GenerateConditions->None] == (- 1)^(n)* LaguerreL[n, \[Beta], x]
Missing Macro Error Failure -
Failed [27 / 27]
Result: Indeterminate
Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[β, 1.5]}

Result: Indeterminate
Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[β, 1.5]}

... skip entries to safe data
18.7.E23 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{\alpha\to\infty}\alpha^{-\frac{1}{2}n}\JacobipolyP{\alpha}{\alpha}{n}@{\alpha^{-\frac{1}{2}}x} = \frac{\HermitepolyH{n}@{x}}{2^{n}n!}}
\lim_{\alpha\to\infty}\alpha^{-\frac{1}{2}n}\JacobipolyP{\alpha}{\alpha}{n}@{\alpha^{-\frac{1}{2}}x} = \frac{\HermitepolyH{n}@{x}}{2^{n}n!}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
limit((alpha)^(-(1)/(2)*n)* JacobiP(n, alpha, alpha, (alpha)^(-(1)/(2))* x), alpha = infinity) = (HermiteH(n, x))/((2)^(n)* factorial(n))
Limit[\[Alpha]^(-Divide[1,2]*n)* JacobiP[n, \[Alpha], \[Alpha], \[Alpha]^(-Divide[1,2])* x], \[Alpha] -> Infinity, GenerateConditions->None] == Divide[HermiteH[n, x],(2)^(n)* (n)!]
Failure Aborted Error Successful [Tested: 9]
18.7.E24 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{\lambda\to\infty}\lambda^{-\frac{1}{2}n}\ultrasphpoly{\lambda}{n}@{\lambda^{-\frac{1}{2}}x} = \frac{\HermitepolyH{n}@{x}}{n!}}
\lim_{\lambda\to\infty}\lambda^{-\frac{1}{2}n}\ultrasphpoly{\lambda}{n}@{\lambda^{-\frac{1}{2}}x} = \frac{\HermitepolyH{n}@{x}}{n!}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
limit((lambda)^(-(1)/(2)*n)* GegenbauerC(n, lambda, (lambda)^(-(1)/(2))* x), lambda = infinity) = (HermiteH(n, x))/(factorial(n))
Limit[\[Lambda]^(-Divide[1,2]*n)* GegenbauerC[n, \[Lambda], \[Lambda]^(-Divide[1,2])* x], \[Lambda] -> Infinity, GenerateConditions->None] == Divide[HermiteH[n, x],(n)!]
Failure Aborted Successful [Tested: 9] Successful [Tested: 9]
18.7.E25 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{\lambda\to 0}\frac{1}{\lambda}\ultrasphpoly{\lambda}{n}@{x} = \frac{2}{n}\ChebyshevpolyT{n}@{x}}
\lim_{\lambda\to 0}\frac{1}{\lambda}\ultrasphpoly{\lambda}{n}@{x} = \frac{2}{n}\ChebyshevpolyT{n}@{x}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n \geq 1}
limit((1)/(lambda)*GegenbauerC(n, lambda, x), lambda = 0) = (2)/(n)*ChebyshevT(n, x)
Limit[Divide[1,\[Lambda]]*GegenbauerC[n, \[Lambda], x], \[Lambda] -> 0, GenerateConditions->None] == Divide[2,n]*ChebyshevT[n, x]
Failure Failure Successful [Tested: 9] Successful [Tested: 9]
18.7.E26 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{\alpha\to\infty}\left(\frac{2}{\alpha}\right)^{\frac{1}{2}n}\LaguerrepolyL[\alpha]{n}@{(2\alpha)^{\frac{1}{2}}x+\alpha} = \frac{(-1)^{n}}{n!}\HermitepolyH{n}@{x}}
\lim_{\alpha\to\infty}\left(\frac{2}{\alpha}\right)^{\frac{1}{2}n}\LaguerrepolyL[\alpha]{n}@{(2\alpha)^{\frac{1}{2}}x+\alpha} = \frac{(-1)^{n}}{n!}\HermitepolyH{n}@{x}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
limit(((2)/(alpha))^((1)/(2)*n)* LaguerreL(n, alpha, (2*alpha)^((1)/(2))* x + alpha), alpha = infinity) = ((- 1)^(n))/(factorial(n))*HermiteH(n, x)
Limit[(Divide[2,\[Alpha]])^(Divide[1,2]*n)* LaguerreL[n, \[Alpha], (2*\[Alpha])^(Divide[1,2])* x + \[Alpha]], \[Alpha] -> Infinity, GenerateConditions->None] == Divide[(- 1)^(n),(n)!]*HermiteH[n, x]
Missing Macro Error Aborted - Successful [Tested: 9]