let-z-from-C-Z-prove-that-pi-sin-piz-1-z-n-1-1-n-2z-z-2-n-2-and-picos-piz-sin-piz-1-z-n-1-2z-z-2-n-2-

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}}