Question Number 28818 by abdo imad last updated on 30/Jan/18
$${prove}\:{that}\:\:\frac{\pi}{\mathrm{4}{cos}\left(\frac{\pi\alpha}{\mathrm{2}}\right)}=\sum_{{p}=\mathrm{0}} ^{\infty} \:\:\:\:\frac{\left(\mathrm{2}{p}+\mathrm{1}\right)\left(−\mathrm{1}\right)^{{p}} }{\left(\mathrm{2}{p}+\mathrm{1}\right)^{\mathrm{2}} \:−\alpha^{\mathrm{2}} } \\ $$$$\alpha\:\in{R}−{Z}. \\ $$