Formula:7566

Digital Library of Mathematical Functions ID 21.3.E3

${\displaystyle{\displaystyle\theta\left(\mathbf{z}+\mathbf{m}_{1}+\boldsymbol{{\Omega}}\mathbf{m}_{2}\middle|\boldsymbol{{\Omega}}\right)=e^{-2\pi i\left(\frac{1}{2}\mathbf{m}_{2}\cdot\boldsymbol{{\Omega}}\cdot\mathbf{m}_{2}+\mathbf{m}_{2}\cdot\mathbf{z}\right)}\theta\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\theta\left(\NVar{\mathbf{z}}\middle|\NVar{\boldsymbol{{\Omega}}}\right)}}$: Riemann theta function
• ${\displaystyle{\displaystyle\pi}}$: 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
 

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