Formula:7483

Digital Library of Mathematical Functions ID 20.6.E4

${\displaystyle{\displaystyle\theta_{3}\left(\pi z\middle|\tau\right)=\theta_{3}\left(0\middle|\tau\right)\exp\left(-\sum_{j=1}^{\infty}\frac{1}{2j}\beta_{2j}(\tau)z^{2j}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle z}}$: complex
• ${\displaystyle{\displaystyle\tau}}$: lattice parameter
• ${\displaystyle{\displaystyle\beta_{2j}(\tau)}}$: coefficient (locally)
 

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