1.8: Difference between revisions
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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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{{DISPLAYTITLE:Algebraic and Analytic Methods - 1.8 Fourier Series}} | |||
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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/1.8.E16 1.8.E16] | | | [https://dlmf.nist.gov/1.8.E16 1.8.E16] || <math qid="Q270">\sum_{n=-\infty}^{\infty}e^{-(n+x)^{2}\omega} = {\sqrt{\frac{\pi}{\omega}}\*\left(1+2\sum_{n=1}^{\infty}e^{-n^{2}\pi^{2}/\omega}\cos@{2n\pi x}\right)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=-\infty}^{\infty}e^{-(n+x)^{2}\omega} = {\sqrt{\frac{\pi}{\omega}}\*\left(1+2\sum_{n=1}^{\infty}e^{-n^{2}\pi^{2}/\omega}\cos@{2n\pi x}\right)}</syntaxhighlight> || <math>\realpart@@{\omega} > 0</math> || <syntaxhighlight lang=mathematica>sum(exp(-(n + x)^(2)* omega), n = - infinity..infinity) = sqrt((Pi)/(omega))*(1 + 2*sum(exp(- (n)^(2)* (Pi)^(2)/omega)*cos(2*n*Pi*x), n = 1..infinity))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Exp[-(n + x)^(2)* \[Omega]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sqrt[Divide[Pi,\[Omega]]]*(1 + 2*Sum[Exp[- (n)^(2)* (Pi)^(2)/\[Omega]]*Cos[2*n*Pi*x], {n, 1, Infinity}, GenerateConditions->None])</syntaxhighlight> || Failure || Successful || Successful [Tested: 15] || Successful [Tested: 15] | ||
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Latest revision as of 10:59, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 1.8.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}e^{-(n+x)^{2}\omega} = {\sqrt{\frac{\pi}{\omega}}\*\left(1+2\sum_{n=1}^{\infty}e^{-n^{2}\pi^{2}/\omega}\cos@{2n\pi x}\right)}}
\sum_{n=-\infty}^{\infty}e^{-(n+x)^{2}\omega} = {\sqrt{\frac{\pi}{\omega}}\*\left(1+2\sum_{n=1}^{\infty}e^{-n^{2}\pi^{2}/\omega}\cos@{2n\pi x}\right)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{\omega} > 0} | sum(exp(-(n + x)^(2)* omega), n = - infinity..infinity) = sqrt((Pi)/(omega))*(1 + 2*sum(exp(- (n)^(2)* (Pi)^(2)/omega)*cos(2*n*Pi*x), n = 1..infinity))
|
Sum[Exp[-(n + x)^(2)* \[Omega]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sqrt[Divide[Pi,\[Omega]]]*(1 + 2*Sum[Exp[- (n)^(2)* (Pi)^(2)/\[Omega]]*Cos[2*n*Pi*x], {n, 1, Infinity}, GenerateConditions->None])
|
Failure | Successful | Successful [Tested: 15] | Successful [Tested: 15] |