21.6: Difference between revisions

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| [https://dlmf.nist.gov/21.6.E6 21.6.E6] || [[Item:Q6894|<math>\Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}-\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}+\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}-\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}} = \frac{1}{2^{g}}\sum_{\boldsymbol{{\alpha}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}\,\sum_{\boldsymbol{{\beta}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}e^{2\pi i\left(2\boldsymbol{{\alpha}}\cdot\boldsymbol{{\Omega}}\cdot\boldsymbol{{\alpha}}+\boldsymbol{{\alpha}}\cdot[\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}]\right)}\*\Riemanntheta@{\mathbf{x}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{y}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{u}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{v}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}-\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}+\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}-\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}} = \frac{1}{2^{g}}\sum_{\boldsymbol{{\alpha}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}\,\sum_{\boldsymbol{{\beta}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}e^{2\pi i\left(2\boldsymbol{{\alpha}}\cdot\boldsymbol{{\Omega}}\cdot\boldsymbol{{\alpha}}+\boldsymbol{{\alpha}}\cdot[\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}]\right)}\*\Riemanntheta@{\mathbf{x}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{y}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{u}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{v}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>RiemannTheta((x + y + u + v)/(2), Omega)*RiemannTheta((x + y - u - v)/(2), Omega)*RiemannTheta((x - y + u - v)/(2), Omega)*RiemannTheta((x - y - u + v)/(2), Omega) = (1)/((2)^(g))*sum(sum(exp(2*Pi*I*(2*alpha * Omega * alpha + alpha *(x + y + u + v)))* RiemannTheta(x + Omega*alpha + beta, Omega)*RiemannTheta(y + Omega*alpha + beta, Omega)*RiemannTheta(u + Omega*alpha + beta, Omega)*RiemannTheta(v + Omega*alpha + beta, Omega),  = ..infinity),  = ..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
| [https://dlmf.nist.gov/21.6.E6 21.6.E6] || <math qid="Q6894">\Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}-\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}+\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}-\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}} = \frac{1}{2^{g}}\sum_{\boldsymbol{{\alpha}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}\,\sum_{\boldsymbol{{\beta}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}e^{2\pi i\left(2\boldsymbol{{\alpha}}\cdot\boldsymbol{{\Omega}}\cdot\boldsymbol{{\alpha}}+\boldsymbol{{\alpha}}\cdot[\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}]\right)}\*\Riemanntheta@{\mathbf{x}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{y}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{u}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{v}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}-\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}+\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}-\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}} = \frac{1}{2^{g}}\sum_{\boldsymbol{{\alpha}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}\,\sum_{\boldsymbol{{\beta}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}e^{2\pi i\left(2\boldsymbol{{\alpha}}\cdot\boldsymbol{{\Omega}}\cdot\boldsymbol{{\alpha}}+\boldsymbol{{\alpha}}\cdot[\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}]\right)}\*\Riemanntheta@{\mathbf{x}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{y}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{u}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{v}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>RiemannTheta((x + y + u + v)/(2), Omega)*RiemannTheta((x + y - u - v)/(2), Omega)*RiemannTheta((x - y + u - v)/(2), Omega)*RiemannTheta((x - y - u + v)/(2), Omega) = (1)/((2)^(g))*sum(sum(exp(2*Pi*I*(2*alpha * Omega * alpha + alpha *(x + y + u + v)))* RiemannTheta(x + Omega*alpha + beta, Omega)*RiemannTheta(y + Omega*alpha + beta, Omega)*RiemannTheta(u + Omega*alpha + beta, Omega)*RiemannTheta(v + Omega*alpha + beta, Omega),  = ..infinity),  = ..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
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Latest revision as of 11:56, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
21.6.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}-\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}+\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}-\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}} = \frac{1}{2^{g}}\sum_{\boldsymbol{{\alpha}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}\,\sum_{\boldsymbol{{\beta}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}e^{2\pi i\left(2\boldsymbol{{\alpha}}\cdot\boldsymbol{{\Omega}}\cdot\boldsymbol{{\alpha}}+\boldsymbol{{\alpha}}\cdot[\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}]\right)}\*\Riemanntheta@{\mathbf{x}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{y}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{u}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{v}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}}
\Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}-\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}+\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}-\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}} = \frac{1}{2^{g}}\sum_{\boldsymbol{{\alpha}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}\,\sum_{\boldsymbol{{\beta}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}e^{2\pi i\left(2\boldsymbol{{\alpha}}\cdot\boldsymbol{{\Omega}}\cdot\boldsymbol{{\alpha}}+\boldsymbol{{\alpha}}\cdot[\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}]\right)}\*\Riemanntheta@{\mathbf{x}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{y}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{u}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{v}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
RiemannTheta((x + y + u + v)/(2), Omega)*RiemannTheta((x + y - u - v)/(2), Omega)*RiemannTheta((x - y + u - v)/(2), Omega)*RiemannTheta((x - y - u + v)/(2), Omega) = (1)/((2)^(g))*sum(sum(exp(2*Pi*I*(2*alpha * Omega * alpha + alpha *(x + y + u + v)))* RiemannTheta(x + Omega*alpha + beta, Omega)*RiemannTheta(y + Omega*alpha + beta, Omega)*RiemannTheta(u + Omega*alpha + beta, Omega)*RiemannTheta(v + Omega*alpha + beta, Omega),  = ..infinity),  = ..infinity)

Error
Missing Macro Error Missing Macro Error - -
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