Question Number 92933 by mathmax by abdo last updated on 09/May/20
$${prove}\:{thst}\:{for}\:{z}\in{C}−{Z}\:\:\:\:\:\left(\frac{\pi{z}}{{sin}\left(\pi{z}\right)}\right)^{\mathrm{2}} \:=\sum_{{n}=−\infty} ^{+\infty} \:\frac{\mathrm{1}}{\left({z}−{n}\right)^{\mathrm{2}} } \\ $$$${and}\:\:\frac{\left(\pi{z}\right)^{\mathrm{2}} }{{sin}^{\mathrm{2}} \left(\pi{z}\right)}{cos}\left(\pi{z}\right)\:=\sum_{{n}=−\infty} ^{+\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left({z}−{n}\right)^{\mathrm{2}} } \\ $$