# Interchange limit and derivative in infinite sum

Suppose we have two functions $$f(x,y)$$, and $$g(x,y)$$ i wish to evaluate the following:

$$$$\frac{\partial}{\partial_y}(\lim_{x\to\infty}f(x,y)\sum_{n=-\infty}^{\infty}e^{-g(x,y)n^2})$$$$

under what conditions can I use the following equality? $$$$\frac{\partial}{\partial_y}(\lim_{x\to\infty}f(x,y)\sum_{n=-\infty}^{\infty}e^{-g(x,y)n^2})=\lim_{x\to\infty}\frac{\partial}{\partial_y}(f(x,y)\sum_{n=-\infty}^{\infty}e^{-g(x,y)n^2})$$$$