# What do we know about $\sum_{n=-\infty}^\infty z^{n^2}$?

If I am asking something stupid, I'm sorry. I was helping one of my academic brother with his course. And I came to this formula:

$$\sum_{n=-\infty}^\infty z^{n^2}=\prod_{m=1}^\infty (1-z^m)(1-z^{m+1/2})^2.$$

I am confused whether the mass inside of the "$\displaystyle\prod_{m=1}^\infty$'' is correct. Shouldn't it be the inverse of the multiplicand?

Thanks for any comment!

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Is it m+1/2 or (m+1)/2. Just a small clarification. –  Gautam Shenoy Nov 19 '12 at 13:26
You might want to look at en.wikipedia.org/wiki/Jacobi_triple_product –  Joel Cohen Nov 19 '12 at 13:40