how to evaluate the following double summation to inifnityinfinity without using integration method?

fixed tex bug

Source Link

edited May 16, 2015 at 20:50

The expression is as follows:

$\sum_{x=0}^{\infty}\sum_{y=0}^{\infty} exp(-\sqrt{x^2+y^2})$$\sum_{x=0}^{\infty}\sum_{y=0}^{\infty} \exp(-\sqrt{x^2+y^2})$

I have thought about using Taylor approximation to get started but it doesn't seem to get me anywhere.

Any hints on how to get started will be appreciated. Thank you in advance.

Source Link

asked May 16, 2015 at 17:28

how to evaluate the following double summation to inifnity without using integration method?

The expression is as follows:

$\sum_{x=0}^{\infty}\sum_{y=0}^{\infty} exp(-\sqrt{x^2+y^2})$

I have thought about using Taylor approximation to get started but it doesn't seem to get me anywhere.

Any hints on how to get started will be appreciated. Thank you in advance.

sequences-and-series