I need help with the following infinite sum: $$\sum_{n=-\infty}^{\infty} \frac{1}{10^{{(n/100)}^2}}$$
It can quite obviously be expressed in terms of the Jacobi Theta Function, but I feel like that is more of a "re-definition" than an actual closed form. There are a few elementary closed forms that may work, but I can't get a very accurate numerical estimate. The approximate numberical value is $\approx 116.589$
How can I derive a closed form for this sum?