Fourier series and partial fraction expansion of πcsc(πz)/z

Asked Nov 05 '22 at 03:54

Active Nov 06 '22 at 19:23

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Having trouble with this question involving the Fourier series and partial fraction expansion.

I need to prove $$ z\sum_{n\in Z }{\frac{(-1)^n}{z^2-n^2} } = π\csc(πz) $$

I think I should start by solving the Fourier series at $z=0$ and $z=π$ and gathering together what is real to get the desired answer.

edited Nov 06 '22 at 19:23

asked Nov 05 '22 at 03:54

Bobby sincaid

Did you mean to type $(-1)^n$? And do you mean $z=0$ and $z=\pi$? – Accelerator Nov 05 '22 at 06:14
1

@Accelerator Yes my mistake! (-1)^n is what I meant and z = 0 and z = π – Bobby sincaid Nov 06 '22 at 19:23
Does this help? – Accelerator Nov 06 '22 at 20:27
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@Accelerator Yes! Thank you! – Bobby sincaid Nov 06 '22 at 23:59

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