Formula:7590

Digital Library of Mathematical Functions ID 21.6.E8

${\displaystyle{\displaystyle\theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\alpha}}}{\boldsymbol{{\gamma}}}\left(\mathbf{z}_{1}\middle|\boldsymbol{{\Omega}}\right)\theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\beta}}}{\boldsymbol{{\delta}}}\left(\mathbf{z}_{2}\middle|\boldsymbol{{\Omega}}\right)=\sum_{\boldsymbol{{\nu}}\in{\mathbb{Z}^{g}}/\left(2{\mathbb{Z}^{g}}\right)}\theta\genfrac{[}{]}{0.0pt}{}{\frac{1}{2}[\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}+\boldsymbol{{\nu}}]}{\boldsymbol{{\gamma}}+\boldsymbol{{\delta}}}\left(\mathbf{z}_{1}+\mathbf{z}_{2}\middle|2\boldsymbol{{\Omega}}\right)\*\theta\genfrac{[}{]}{0.0pt}{}{\frac{1}{2}[\boldsymbol{{\alpha}}-\boldsymbol{{\beta}}+\boldsymbol{{\nu}}]}{\boldsymbol{{\gamma}}-\boldsymbol{{\delta}}}\left(\mathbf{z}_{1}-\mathbf{z}_{2}\middle|2\boldsymbol{{\Omega}}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\theta\genfrac{[}{]}{0.0pt}{}{\NVar{\boldsymbol{{\alpha}}}}{\NVar{\boldsymbol{{\beta}}}}\left(\middle|missing\right)\)\@add@PDF@RDFa@triples\end{document}}}$: Riemann theta function with characteristics
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\mathbb{Z}}}$:
• ${\displaystyle{\displaystyle g}}$: positive integer
• ${\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}$: a Riemann matrix
• ${\displaystyle{\displaystyle\boldsymbol{{\alpha}}}}$: g -dimensional vector
• ${\displaystyle{\displaystyle\boldsymbol{{\beta}}}}$: g -dimensional vector
• ${\displaystyle{\displaystyle\boldsymbol{{\delta}}}}$: g -dimensional vector
• ${\displaystyle{\displaystyle\boldsymbol{{\gamma}}}}$: g -dimensional vector
 

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