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Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
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! DLMF !! Formula !! Constraints !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica | ! DLMF !! style=width:20em | Formula !! Constraints !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica | ||
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| [https://dlmf.nist.gov/1.2.E1 1.2.E1] || [[Item:Q30|<math>\binom{n}{k} = \frac{n!}{(n-k)!k!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 80%;" inline>\binom{n}{k} = \frac{n!}{(n-k)!k!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>binomial(n,k) = (factorial(n))/(factorial(n - k)*factorial(k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Binomial[n,k] == Divide[(n)!,(n - k)!*(k)!]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9] | | [https://dlmf.nist.gov/1.2.E1 1.2.E1] || [[Item:Q30|<math>\binom{n}{k} = \frac{n!}{(n-k)!k!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 80%;" inline>\binom{n}{k} = \frac{n!}{(n-k)!k!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>binomial(n,k) = (factorial(n))/(factorial(n - k)*factorial(k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Binomial[n,k] == Divide[(n)!,(n - k)!*(k)!]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9] | ||
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| [https://dlmf.nist.gov/18.35.E4 18.35.E4] || [[Item:Q6043|<math>\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n}}{n!}e^{\iunit n\theta}\*\genhyperF{2}{1}@@{-n,\lambda+\iunit\tau_{a,b}(\theta)}{-n-\lambda+1+\iunit\tau_{a,b}(\theta)}{e^{-2\iunit\theta}} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda+\iunit\tau_{a,b}(\theta)}{\ell}}{\ell!}\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n-\ell}}{(n-\ell)!}e^{\iunit(n-2\ell)\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n}}{n!}e^{\iunit n\theta}\*\genhyperF{2}{1}@@{-n,\lambda+\iunit\tau_{a,b}(\theta)}{-n-\lambda+1+\iunit\tau_{a,b}(\theta)}{e^{-2\iunit\theta}} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda+\iunit\tau_{a,b}(\theta)}{\ell}}{\ell!}\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n-\ell}}{(n-\ell)!}e^{\iunit(n-2\ell)\theta}</syntaxhighlight> || <math>0 < \theta, \theta < \pi</math> || <syntaxhighlight lang=mathematica>(pochhammer(lambda - I*((a*cos(theta)+ b)/(sin(theta))), n))/(factorial(n))*exp(I*n*theta)* hypergeom([- n , lambda + I*((a*cos(theta)+ b)/(sin(theta)))], [- n - lambda + 1 + I*((a*cos(theta)+ b)/(sin(theta)))], exp(- 2*I*theta)) = sum((pochhammer(lambda + I*((a*cos(theta)+ b)/(sin(theta))), ell))/(factorial(ell))*(pochhammer(lambda - I*((a*cos(theta)+ b)/(sin(theta))), n - ell))/(factorial(n - ell))*exp(I*(n - 2*ell)*theta), ell = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Pochhammer[\[Lambda]- I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), n],(n)!]*Exp[I*n*\[Theta]]* HypergeometricPFQ[{- n , \[Lambda]+ I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])}, {- n - \[Lambda]+ 1 + I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])}, Exp[- 2*I*\[Theta]]] == Sum[Divide[Pochhammer[\[Lambda]+ I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), \[ScriptL]],(\[ScriptL])!]*Divide[Pochhammer[\[Lambda]- I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), n - \[ScriptL]],(n - \[ScriptL])!]*Exp[I*(n - 2*\[ScriptL])*\[Theta]], {\[ScriptL], 0, n}, GenerateConditions->None]</syntaxhighlight> || Error || Successful || - || Successful [Tested: 300] | |||
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Revision as of 07:39, 18 May 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 1.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{n}{k} = \frac{n!}{(n-k)!k!}}
\binom{n}{k} = \frac{n!}{(n-k)!k!} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | binomial(n,k) = (factorial(n))/(factorial(n - k)*factorial(k))
|
Binomial[n,k] == Divide[(n)!,(n - k)!*(k)!]
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Successful | Successful | - | Successful [Tested: 9] |
| 18.35.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n}}{n!}e^{\iunit n\theta}\*\genhyperF{2}{1}@@{-n,\lambda+\iunit\tau_{a,b}(\theta)}{-n-\lambda+1+\iunit\tau_{a,b}(\theta)}{e^{-2\iunit\theta}} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda+\iunit\tau_{a,b}(\theta)}{\ell}}{\ell!}\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n-\ell}}{(n-\ell)!}e^{\iunit(n-2\ell)\theta}}
\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n}}{n!}e^{\iunit n\theta}\*\genhyperF{2}{1}@@{-n,\lambda+\iunit\tau_{a,b}(\theta)}{-n-\lambda+1+\iunit\tau_{a,b}(\theta)}{e^{-2\iunit\theta}} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda+\iunit\tau_{a,b}(\theta)}{\ell}}{\ell!}\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n-\ell}}{(n-\ell)!}e^{\iunit(n-2\ell)\theta} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < \theta, \theta < \pi} | (pochhammer(lambda - I*((a*cos(theta)+ b)/(sin(theta))), n))/(factorial(n))*exp(I*n*theta)* hypergeom([- n , lambda + I*((a*cos(theta)+ b)/(sin(theta)))], [- n - lambda + 1 + I*((a*cos(theta)+ b)/(sin(theta)))], exp(- 2*I*theta)) = sum((pochhammer(lambda + I*((a*cos(theta)+ b)/(sin(theta))), ell))/(factorial(ell))*(pochhammer(lambda - I*((a*cos(theta)+ b)/(sin(theta))), n - ell))/(factorial(n - ell))*exp(I*(n - 2*ell)*theta), ell = 0..n)
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Divide[Pochhammer[\[Lambda]- I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), n],(n)!]*Exp[I*n*\[Theta]]* HypergeometricPFQ[{- n , \[Lambda]+ I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])}, {- n - \[Lambda]+ 1 + I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])}, Exp[- 2*I*\[Theta]]] == Sum[Divide[Pochhammer[\[Lambda]+ I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), \[ScriptL]],(\[ScriptL])!]*Divide[Pochhammer[\[Lambda]- I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), n - \[ScriptL]],(n - \[ScriptL])!]*Exp[I*(n - 2*\[ScriptL])*\[Theta]], {\[ScriptL], 0, n}, GenerateConditions->None]
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Error | Successful | - | Successful [Tested: 300] |