# An infinite sum

1. Sep 28, 2014

### tom.stoer

Does anybody know a closed for

$$f(A,B) = \sum_{n\in\mathbb{Z}}e^{-Bn^2 + iAn}$$

with A real and B positive.

2. Sep 28, 2014

### Staff: Mentor

3. Sep 28, 2014

### tom.stoer

I can't believe that.
I tried to calculate the density operator in position rep. for a particle on a circle. You get the exp(iAn) term from the eigenfunctions on the circle; A contains the angle. And you get the exp(-Bn2) from exp(-H/T).
So it's nothing exotic.

4. Sep 28, 2014

### tom.stoer

Last edited: Sep 28, 2014