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I need to prove

$$\sum_{n=1}^{+\infty}\frac{1}{n^2-\alpha^2}=\frac{1}{2\alpha^2}-\frac{\pi}{2\alpha\tan(\alpha\pi)},$$

with $\alpha$ a non integer complex.

I know that I have to use the Parseval's Indentity relation but I don't know whose function's expansion makes this possible.

Ahaan S. Rungta
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José
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  • For reasons explained here, this is the same as showing that $$\int_0^1\frac{x^a-x^{-a}}{1-x}dx=\pi\cot\pi a-\frac1a$$ – Lucian Dec 05 '13 at 12:45

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