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

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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.

Please help me!