What is the double sum of: $\sum\limits_{n=0}^\infty \sum\limits_{m=0}^\infty \frac{ \sin[ka(m-n)]}{(m-n)} , m \neq n $
where $k$ and $a$ are constants.
How to treat this double sum?
Hint: Use the fact that $$\frac{\sin[(m-n)ka]}{m-n} = \frac 1 2\int_{-ka}^{ka}e^{i(m-n)t}dt$$
This is what i got.
If there is any error, let me know, please.