View source for 21.2

{{DISPLAYTITLE:Theta Functions - 21.2 Definitions}}

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! scope="col" style="position: sticky; top: 0;" | Formula 
! scope="col" style="position: sticky; top: 0;" | Constraints 
! scope="col" style="position: sticky; top: 0;" | Maple
! scope="col" style="position: sticky; top: 0;" | Mathematica
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! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/21.2.E1 21.2.E1] || <math qid="Q6857">\Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}} = \sum_{\mathbf{n}\in\Integers^{g}}e^{2\pi i\left(\frac{1}{2}\mathbf{n}\cdot\boldsymbol{{\Omega}}\cdot\mathbf{n}+\mathbf{n}\cdot\mathbf{z}\right)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}} = \sum_{\mathbf{n}\in\Integers^{g}}e^{2\pi i\left(\frac{1}{2}\mathbf{n}\cdot\boldsymbol{{\Omega}}\cdot\mathbf{n}+\mathbf{n}\cdot\mathbf{z}\right)}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>RiemannTheta(z, Omega) = sum(exp(2*Pi*I*((1)/(2)*n * Omega * n + n * z)),  = ..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
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| [https://dlmf.nist.gov/21.2.E8 21.2.E8] || <math qid="Q6864">\Riemanntheta@{z}{\Omega} = \Jacobithetatau{3}@{\pi z}{\Omega}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Riemanntheta@{z}{\Omega} = \Jacobithetatau{3}@{\pi z}{\Omega}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>RiemannTheta(z, Omega) = JacobiTheta3(Pi*z,exp(I*Pi*Omega))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
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