# Closed form of $\sum_{n=1}^\infty q^{- n^2} z^n$

In this question the summation goes from $$-\infty$$ to $$\infty$$ and the answer has a pretty "good" closed form.

Now I came across the sum $$\sum_{n=1}^\infty q^{-n^2} z^n$$ where $$|z|<1$$ and I don't know how to crack it.