2
$\begingroup$

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

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

under what conditions can I use the following equality? \begin{equation} \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}) \end{equation}

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.