Homework Statement
I need to find a closed form for what at first light would be a straightforward finite series. Calculating it explicitly to a particular degree is not difficult, but I just can't find the closed form for the general case.
Homework Equations
For N>m, the series is...
1. I want to find a close expression for the following infinite sum
\sum_{n=1}^{\infty}\left(\frac{1}{\sqrt{n^2+x_1 y}}-\frac{1}{\sqrt{n^2+x_2 y}}\right)
Both x_i and y are greater than 0.
The Attempt at a Solution
I haven't got much really. I realize each sum independently is...