Formula:7568

Digital Library of Mathematical Functions ID 21.3.E5

${\displaystyle{\displaystyle\theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\alpha}}}{\boldsymbol{{\beta}}}\left(\mathbf{z}+\mathbf{m}_{1}+\boldsymbol{{\Omega}}\mathbf{m}_{2}\middle|\boldsymbol{{\Omega}}\right)=e^{2\pi i\left(\boldsymbol{{\alpha}}\cdot\mathbf{m}_{1}-\boldsymbol{{\beta}}\cdot\mathbf{m}_{2}-\frac{1}{2}\mathbf{m}_{2}\cdot\boldsymbol{{\Omega}}\cdot\mathbf{m}_{2}-\mathbf{m}_{2}\cdot\mathbf{z}\right)}\theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\alpha}}}{\boldsymbol{{\beta}}}\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right).}}$

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
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}$: a Riemann matrix
• ${\displaystyle{\displaystyle\boldsymbol{{\alpha}}}}$: g -dimensional vector
• ${\displaystyle{\displaystyle\boldsymbol{{\beta}}}}$: g -dimensional vector
 

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