I am a physicist, and working on some project I have found this series:
$$ S(t) = \sum_{n=1}^{\infty} \frac{e^{-tn^2}}{n^2} $$
so that $S(0) = \frac{\pi^2}{6}$, the classic Euler problem.
Sadly, this series does not admit an easy solution using the complex integral trick for general $t$, for example. But I am sure someone must have found a name for this, or is just one case of some generalized zeta function (or maybe a Jacobi function?).
I am digging through Wikipedia, but I haven't been able to find anything exactly like this yet. Does anyone know how to express it in terms of other known functions?