Formula:7479

Digital Library of Mathematical Functions ID 20.5.E17

${\displaystyle{\displaystyle\theta_{4}\left(z\middle|\tau\right)=\theta_{4}\left(0\middle|\tau\right)\*\lim_{N\to\infty}\prod_{n=1-N}^{N}\lim_{M\to\infty}\prod_{m=-M}^{M}\left(1+\frac{z}{(m+(n-\tfrac{1}{2})\tau)\pi}\right).}}$

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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