I would like to know the behaviour of $\vartheta_4$ listed here about $q=1$. The Jacobi theta function is undefined at $q=1$. Is it possible to calculate a Laurent series? If so, how would you go about finding this? Do you know of any other ways I can get a simple expression which closely approximates the value of $\vartheta_4$ for $q$ close 1?
2026-03-25 02:59:29.1774407569
Laurent series for a Jacobi Theta function?
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