18.6: Difference between revisions

From testwiki
Jump to navigation Jump to search
VisualWikitext
 
 
Line 14: Line 14:
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
|-  
|-  
| [https://dlmf.nist.gov/18.6.E1 18.6.E1] || [[Item:Q5564|<math>\LaguerrepolyL[\alpha]{n}@{0} = \frac{\Pochhammersym{\alpha+1}{n}}{n!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\LaguerrepolyL[\alpha]{n}@{0} = \frac{\Pochhammersym{\alpha+1}{n}}{n!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LaguerreL(n, alpha, 0) = (pochhammer(alpha + 1, n))/(factorial(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>LaguerreL[n, \[Alpha], 0] == Divide[Pochhammer[\[Alpha]+ 1, n],(n)!]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 9]
| [https://dlmf.nist.gov/18.6.E1 18.6.E1] || <math qid="Q5564">\LaguerrepolyL[\alpha]{n}@{0} = \frac{\Pochhammersym{\alpha+1}{n}}{n!}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\LaguerrepolyL[\alpha]{n}@{0} = \frac{\Pochhammersym{\alpha+1}{n}}{n!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LaguerreL(n, alpha, 0) = (pochhammer(alpha + 1, n))/(factorial(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>LaguerreL[n, \[Alpha], 0] == Divide[Pochhammer[\[Alpha]+ 1, n],(n)!]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 9]
|-  
|-  
| [https://dlmf.nist.gov/18.6.E2 18.6.E2] || [[Item:Q5565|<math>\lim_{\alpha\to\infty}\frac{\JacobipolyP{\alpha}{\beta}{n}@{x}}{\JacobipolyP{\alpha}{\beta}{n}@{1}} = \left(\frac{1+x}{2}\right)^{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\alpha\to\infty}\frac{\JacobipolyP{\alpha}{\beta}{n}@{x}}{\JacobipolyP{\alpha}{\beta}{n}@{1}} = \left(\frac{1+x}{2}\right)^{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((JacobiP(n, alpha, beta, x))/(JacobiP(n, alpha, beta, 1)), alpha = infinity) = ((1 + x)/(2))^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[JacobiP[n, \[Alpha], \[Beta], x],JacobiP[n, \[Alpha], \[Beta], 1]], \[Alpha] -> Infinity, GenerateConditions->None] == (Divide[1 + x,2])^(n)</syntaxhighlight> || Failure || Aborted || Successful [Tested: 27] || Skipped - Because timed out
| [https://dlmf.nist.gov/18.6.E2 18.6.E2] || <math qid="Q5565">\lim_{\alpha\to\infty}\frac{\JacobipolyP{\alpha}{\beta}{n}@{x}}{\JacobipolyP{\alpha}{\beta}{n}@{1}} = \left(\frac{1+x}{2}\right)^{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\alpha\to\infty}\frac{\JacobipolyP{\alpha}{\beta}{n}@{x}}{\JacobipolyP{\alpha}{\beta}{n}@{1}} = \left(\frac{1+x}{2}\right)^{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((JacobiP(n, alpha, beta, x))/(JacobiP(n, alpha, beta, 1)), alpha = infinity) = ((1 + x)/(2))^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[JacobiP[n, \[Alpha], \[Beta], x],JacobiP[n, \[Alpha], \[Beta], 1]], \[Alpha] -> Infinity, GenerateConditions->None] == (Divide[1 + x,2])^(n)</syntaxhighlight> || Failure || Aborted || Successful [Tested: 27] || Skipped - Because timed out
|-  
|-  
| [https://dlmf.nist.gov/18.6.E3 18.6.E3] || [[Item:Q5566|<math>\lim_{\beta\to\infty}\frac{\JacobipolyP{\alpha}{\beta}{n}@{x}}{\JacobipolyP{\alpha}{\beta}{n}@{-1}} = \left(\frac{1-x}{2}\right)^{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\beta\to\infty}\frac{\JacobipolyP{\alpha}{\beta}{n}@{x}}{\JacobipolyP{\alpha}{\beta}{n}@{-1}} = \left(\frac{1-x}{2}\right)^{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((JacobiP(n, alpha, beta, x))/(JacobiP(n, alpha, beta, - 1)), beta = infinity) = ((1 - x)/(2))^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[JacobiP[n, \[Alpha], \[Beta], x],JacobiP[n, \[Alpha], \[Beta], - 1]], \[Beta] -> Infinity, GenerateConditions->None] == (Divide[1 - x,2])^(n)</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 27]
| [https://dlmf.nist.gov/18.6.E3 18.6.E3] || <math qid="Q5566">\lim_{\beta\to\infty}\frac{\JacobipolyP{\alpha}{\beta}{n}@{x}}{\JacobipolyP{\alpha}{\beta}{n}@{-1}} = \left(\frac{1-x}{2}\right)^{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\beta\to\infty}\frac{\JacobipolyP{\alpha}{\beta}{n}@{x}}{\JacobipolyP{\alpha}{\beta}{n}@{-1}} = \left(\frac{1-x}{2}\right)^{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((JacobiP(n, alpha, beta, x))/(JacobiP(n, alpha, beta, - 1)), beta = infinity) = ((1 - x)/(2))^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[JacobiP[n, \[Alpha], \[Beta], x],JacobiP[n, \[Alpha], \[Beta], - 1]], \[Beta] -> Infinity, GenerateConditions->None] == (Divide[1 - x,2])^(n)</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 27]
|-  
|-  
| [https://dlmf.nist.gov/18.6.E4 18.6.E4] || [[Item:Q5567|<math>\lim_{\lambda\to\infty}\frac{\ultrasphpoly{\lambda}{n}@{x}}{\ultrasphpoly{\lambda}{n}@{1}} = x^{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\lambda\to\infty}\frac{\ultrasphpoly{\lambda}{n}@{x}}{\ultrasphpoly{\lambda}{n}@{1}} = x^{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((GegenbauerC(n, lambda, x))/(GegenbauerC(n, lambda, 1)), lambda = infinity) = (x)^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[GegenbauerC[n, \[Lambda], x],GegenbauerC[n, \[Lambda], 1]], \[Lambda] -> Infinity, GenerateConditions->None] == (x)^(n)</syntaxhighlight> || Failure || Aborted || Successful [Tested: 9] || Skipped - Because timed out
| [https://dlmf.nist.gov/18.6.E4 18.6.E4] || <math qid="Q5567">\lim_{\lambda\to\infty}\frac{\ultrasphpoly{\lambda}{n}@{x}}{\ultrasphpoly{\lambda}{n}@{1}} = x^{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\lambda\to\infty}\frac{\ultrasphpoly{\lambda}{n}@{x}}{\ultrasphpoly{\lambda}{n}@{1}} = x^{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((GegenbauerC(n, lambda, x))/(GegenbauerC(n, lambda, 1)), lambda = infinity) = (x)^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[GegenbauerC[n, \[Lambda], x],GegenbauerC[n, \[Lambda], 1]], \[Lambda] -> Infinity, GenerateConditions->None] == (x)^(n)</syntaxhighlight> || Failure || Aborted || Successful [Tested: 9] || Skipped - Because timed out
|-  
|-  
| [https://dlmf.nist.gov/18.6.E5 18.6.E5] || [[Item:Q5568|<math>\lim_{\alpha\to\infty}\frac{\LaguerrepolyL[\alpha]{n}@{\alpha x}}{\LaguerrepolyL[\alpha]{n}@{0}} = (1-x)^{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\alpha\to\infty}\frac{\LaguerrepolyL[\alpha]{n}@{\alpha x}}{\LaguerrepolyL[\alpha]{n}@{0}} = (1-x)^{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((LaguerreL(n, alpha, alpha*x))/(LaguerreL(n, alpha, 0)), alpha = infinity) = (1 - x)^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[LaguerreL[n, \[Alpha], \[Alpha]*x],LaguerreL[n, \[Alpha], 0]], \[Alpha] -> Infinity, GenerateConditions->None] == (1 - x)^(n)</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
| [https://dlmf.nist.gov/18.6.E5 18.6.E5] || <math qid="Q5568">\lim_{\alpha\to\infty}\frac{\LaguerrepolyL[\alpha]{n}@{\alpha x}}{\LaguerrepolyL[\alpha]{n}@{0}} = (1-x)^{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{\alpha\to\infty}\frac{\LaguerrepolyL[\alpha]{n}@{\alpha x}}{\LaguerrepolyL[\alpha]{n}@{0}} = (1-x)^{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((LaguerreL(n, alpha, alpha*x))/(LaguerreL(n, alpha, 0)), alpha = infinity) = (1 - x)^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[LaguerreL[n, \[Alpha], \[Alpha]*x],LaguerreL[n, \[Alpha], 0]], \[Alpha] -> Infinity, GenerateConditions->None] == (1 - x)^(n)</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
|}
|}
</div>
</div>

Latest revision as of 11:44, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
18.6.E1 L n ( α ) ⁡ ( 0 ) = ( α + 1 ) n n ! Laguerre-polynomial-L 𝛼 𝑛 0 Pochhammer 𝛼 1 𝑛 𝑛 {\displaystyle{\displaystyle L^{(\alpha)}_{n}\left(0\right)=\frac{{\left(% \alpha+1\right)_{n}}}{n!}}}
\LaguerrepolyL[\alpha]{n}@{0} = \frac{\Pochhammersym{\alpha+1}{n}}{n!}		 

LaguerreL(n, alpha, 0) = (pochhammer(alpha + 1, n))/(factorial(n))

LaguerreL[n, \[Alpha], 0] == Divide[Pochhammer[\[Alpha]+ 1, n],(n)!]
Missing Macro Error Successful - Successful [Tested: 9]
18.6.E2 lim α → ∞ ⁡ P n ( α , β ) ⁡ ( x ) P n ( α , β ) ⁡ ( 1 ) = ( 1 + x 2 ) n subscript → 𝛼 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 superscript 1 𝑥 2 𝑛 {\displaystyle{\displaystyle\lim_{\alpha\to\infty}\frac{P^{(\alpha,\beta)}_{n}% \left(x\right)}{P^{(\alpha,\beta)}_{n}\left(1\right)}=\left(\frac{1+x}{2}% \right)^{n}}}
\lim_{\alpha\to\infty}\frac{\JacobipolyP{\alpha}{\beta}{n}@{x}}{\JacobipolyP{\alpha}{\beta}{n}@{1}} = \left(\frac{1+x}{2}\right)^{n}		 

limit((JacobiP(n, alpha, beta, x))/(JacobiP(n, alpha, beta, 1)), alpha = infinity) = ((1 + x)/(2))^(n)

Limit[Divide[JacobiP[n, \[Alpha], \[Beta], x],JacobiP[n, \[Alpha], \[Beta], 1]], \[Alpha] -> Infinity, GenerateConditions->None] == (Divide[1 + x,2])^(n)
Failure Aborted Successful [Tested: 27] Skipped - Because timed out
18.6.E3 lim β → ∞ ⁡ P n ( α , β ) ⁡ ( x ) P n ( α , β ) ⁡ ( - 1 ) = ( 1 - x 2 ) n subscript → 𝛽 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 superscript 1 𝑥 2 𝑛 {\displaystyle{\displaystyle\lim_{\beta\to\infty}\frac{P^{(\alpha,\beta)}_{n}% \left(x\right)}{P^{(\alpha,\beta)}_{n}\left(-1\right)}=\left(\frac{1-x}{2}% \right)^{n}}}
\lim_{\beta\to\infty}\frac{\JacobipolyP{\alpha}{\beta}{n}@{x}}{\JacobipolyP{\alpha}{\beta}{n}@{-1}} = \left(\frac{1-x}{2}\right)^{n}		 

limit((JacobiP(n, alpha, beta, x))/(JacobiP(n, alpha, beta, - 1)), beta = infinity) = ((1 - x)/(2))^(n)

Limit[Divide[JacobiP[n, \[Alpha], \[Beta], x],JacobiP[n, \[Alpha], \[Beta], - 1]], \[Beta] -> Infinity, GenerateConditions->None] == (Divide[1 - x,2])^(n)
Failure Failure Error Successful [Tested: 27]
18.6.E4 lim λ → ∞ ⁡ C n ( λ ) ⁡ ( x ) C n ( λ ) ⁡ ( 1 ) = x n subscript → 𝜆 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 1 superscript 𝑥 𝑛 {\displaystyle{\displaystyle\lim_{\lambda\to\infty}\frac{C^{(\lambda)}_{n}% \left(x\right)}{C^{(\lambda)}_{n}\left(1\right)}=x^{n}}}
\lim_{\lambda\to\infty}\frac{\ultrasphpoly{\lambda}{n}@{x}}{\ultrasphpoly{\lambda}{n}@{1}} = x^{n}		 

limit((GegenbauerC(n, lambda, x))/(GegenbauerC(n, lambda, 1)), lambda = infinity) = (x)^(n)

Limit[Divide[GegenbauerC[n, \[Lambda], x],GegenbauerC[n, \[Lambda], 1]], \[Lambda] -> Infinity, GenerateConditions->None] == (x)^(n)
Failure Aborted Successful [Tested: 9] Skipped - Because timed out
18.6.E5 lim α → ∞ ⁡ L n ( α ) ⁡ ( α ⁢ x ) L n ( α ) ⁡ ( 0 ) = ( 1 - x ) n subscript → 𝛼 Laguerre-polynomial-L 𝛼 𝑛 𝛼 𝑥 Laguerre-polynomial-L 𝛼 𝑛 0 superscript 1 𝑥 𝑛 {\displaystyle{\displaystyle\lim_{\alpha\to\infty}\frac{L^{(\alpha)}_{n}\left(% \alpha x\right)}{L^{(\alpha)}_{n}\left(0\right)}=(1-x)^{n}}}
\lim_{\alpha\to\infty}\frac{\LaguerrepolyL[\alpha]{n}@{\alpha x}}{\LaguerrepolyL[\alpha]{n}@{0}} = (1-x)^{n}		 

limit((LaguerreL(n, alpha, alpha*x))/(LaguerreL(n, alpha, 0)), alpha = infinity) = (1 - x)^(n)

Limit[Divide[LaguerreL[n, \[Alpha], \[Alpha]*x],LaguerreL[n, \[Alpha], 0]], \[Alpha] -> Infinity, GenerateConditions->None] == (1 - x)^(n)
Missing Macro Error Aborted - Skipped - Because timed out
Retrieved from "https://lct.wmflabs.org/w/index.php?title=18.6&oldid=58335"