I'm trying to solve a set of equations numerically - mainly because I believe it's not possible to do it analytically. The problem is that they involve expressions of the form
$\sum_{k=1}^{\infty} \exp(-Ak^2+Bk)$
where $A$ and $B$ are constants. I was hoping to be able to rewrite this in function of $\textit{Jacobi theta}$ functions, but this seems hard when $k$ does not run to minus infinity as well. Is there some way to rewrite this in terms of theta functions or other functions that have been studied before? This would make it possible to exploit some of their known properties, and possibly speed up the numerical work.
Thanks!