let z from C−Z prove that (π/(sin(πz))) =(1/z) +Σ_(n=1) ^∞ (((−1)^n 2z)/(z^2 −n^2 )) and ((πcos(πz))/(sin(πz))) =(1/z) +Σ


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Question Number 67522 by mathmax by abdo last updated on 28/Aug/19

$l e t z f r o m C - Z p r o v e t h a t$ $\frac{π}{s i n (π z)} = \frac{1}{z} + \sum_{n = 1}^{\infty} \frac{{(- 1)}^{n} 2 z}{z^{2} - n^{2}} a n d$ $\frac{π c o s (π z)}{s i n (π z)} = \frac{1}{z} + \sum_{n = 1}^{\infty} \frac{2 z}{z^{2} - n^{2}}$
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