Formula:7477

Digital Library of Mathematical Functions ID 20.5.E15

${\displaystyle{\displaystyle\theta_{2}\left(z\middle|\tau\right)=\theta_{2}\left(0\middle|\tau\right)\*\lim_{N\to\infty}\prod_{n=-N}^{N}\lim_{M\to\infty}\prod_{m=1-M}^{M}\left(1+\frac{z}{(m-\tfrac{1}{2}+n\tau)\pi}\right),}}$

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
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle z}}$: complex
• ${\displaystyle{\displaystyle\tau}}$: lattice parameter
 

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