Formula:7555

Digital Library of Mathematical Functions ID 21.2.E4

${\displaystyle{\displaystyle\hat{\theta}\left(x_{1}+iy_{1},x_{2}+iy_{2}\middle|\begin{bmatrix}i&-\tfrac{1}{2}\\ -\tfrac{1}{2}&i\end{bmatrix}\right)=\sum_{n_{1}=-\infty}^{\infty}\sum_{n_{2}=-\infty}^{\infty}e^{-\pi(n_{1}+y_{1})^{2}-\pi(n_{2}+y_{2})^{2}}\*e^{\pi i(2n_{1}x_{1}+2n_{2}x_{2}-n_{1}n_{2})}.}}$

Symbols List

• ${\displaystyle{\displaystyle\hat{\theta}\left(\NVar{\mathbf{z}}\middle|\NVar{\boldsymbol{{\Omega}}}\right)}}$: scaled 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
 

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