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Is the $z\gg 1$ behavior of the theta function $\theta_1(z;q)$ known? It seems naively like it could be estimated by a Gaussian integral which would give an answer along the lines of $e^{bz^2}$ for some $b$. I have had no luck finding the answer anywhere.

Thanks!

user245692
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  • The theta functions are periodic in $z$, normally with period $2\pi$, so there isn't a distinction possible between large and small $z$. – Chappers Jun 04 '15 at 02:07

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