I have a sum of the form

$$\sum\_{n,m=-N}^N e^{-\alpha (n-m)^2}$$

where $α>0$ is some constant, and I don't mind if the limit $N\rightarrow\infty$ is taken. I know there is a possibility of exchanging the "variable of summation" by introducing some "relative coordinates" $\tau=n−m$ and $\eta=m+n$, but I don't know how to continue from there.