How to show the following identity holds?
$ \displaystyle\sum_{n=1}^\infty\dfrac{2z}{z^2-n^2}=\pi\cot \pi z-\dfrac{1}{z}\qquad |z|<1 $
How to show the following identity holds?
$ \displaystyle\sum_{n=1}^\infty\dfrac{2z}{z^2-n^2}=\pi\cot \pi z-\dfrac{1}{z}\qquad |z|<1 $
I have found a link which deals with this problem: people.reed.edu/~jerry/311/cotan.pdf