1.8: 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/1.8.E16 1.8.E16] || [[Item:Q270|<math>\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]
| [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 ∑ n = - ∞ ∞ e - ( n + x ) 2 ⁢ ω = π ω ⁢ ( 1 + 2 ⁢ ∑ n = 1 ∞ e - n 2 ⁢ π 2 / ω ⁢ cos ⁡ ( 2 ⁢ n ⁢ π ⁢ x ) ) superscript subscript 𝑛 superscript 𝑒 superscript 𝑛 𝑥 2 𝜔 𝜋 𝜔 1 2 superscript subscript 𝑛 1 superscript 𝑒 superscript 𝑛 2 superscript 𝜋 2 𝜔 2 𝑛 𝜋 𝑥 {\displaystyle{\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\left(2n\pi x\right)\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)}		 ℜ ⁡ ω > 0 𝜔 0 {\displaystyle{\displaystyle\Re\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]
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