I have a infinite sum which I wonder if it will converge to a simpler function
$f(r) = \Sigma_n r^{n^2} , r<1$,
I also interested in case $r$ is a complex number on unity circle $r = e^{j\omega}$.
2026-03-25 23:10:41.1774480241
Sum of exponential square series
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By definition, $\displaystyle\sum_{n=-\infty}^\infty r^{n^2}=\theta_3(0,r)$. See Jacobi elliptic $\theta$ function.