Formula:7557

Digital Library of Mathematical Functions ID 21.2.E6

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \Riemannthetachar{\boldsymbol{{\alpha}}}{\boldsymbol{{\beta}}}@{\mathbf{z}}{\boldsymbol{{\Omega}}}=e^{2\pi i\left(\frac{1}{2}\boldsymbol{{\alpha}}\cdot\boldsymbol{{\Omega}}\cdot\boldsymbol{{\alpha}}+\boldsymbol{{\alpha}}\cdot[\mathbf{z}+\boldsymbol{{\beta}}]\right)}\Riemanntheta@{\mathbf{z}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}},}

Symbols List

• ${\displaystyle{\displaystyle\theta\left(\NVar{\mathbf{z}}\middle|\NVar{\boldsymbol{{\Omega}}}\right)}}$: Riemann theta function
• ${\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
• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \cpi} : 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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