I was reading on the theta function $$ \vartheta(x) = \sum_{n=-\infty}^\infty e^{-\pi n^2 x}\qquad x>0 $$ The author claims that $\vartheta$ is smooth. Is there an easy way to show that this is indeed the case?
Thanks in advance!
2026-02-22 20:39:15.1771792755
How to show that the theta function is smooth?
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