Originally Posted by

**mundhadashantanu** Hi All,

This is my first thread so please forgive any mistakes regarding forum rules.

I have been trying to do some calculations for my Physics project. And I get stuck at following summations,

1. $\displaystyle \sum_{n=-\infty}^{\infty}\exp{\left(-\alpha n^2\right)}$

2. $\displaystyle \sum_{n=-\infty}^{\infty}n^2\exp{\left(-\alpha n^2\right)}$

3. $\displaystyle \sum_{n=-\infty}^{\infty}(-1)^n\exp{\left(-\alpha n^2\right)}$

We have already tried to approximate the summations as an integration of Gaussian. Apparently this is not good enough approximation for our purpose. Any help or suggestions will be appreciated. The first one seems to be key for other two.

Regards,

Shantanu