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I found on a book of QFT in curved spacetime (Birrel and Davies, pag 53) the following identity

[tex]

cosec^2 \pi x = \frac{1}{sin^2 \pi x} = \pi^{-2} \sum_{k=-\infty}^{+\infty} \frac{1}{(x-k)^2}

[/tex]

Can anyone help to derive it or give some reference to a book for the proof. I have no idea of how prove this....

Thanks