prove-that-pi-4cos-pi-2-p-0-2p-1-1-p-2p-1-2-2-R-Z-

Tinku Tara June 4, 2023 Limits 0 Comments

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Question Number 28818 by abdo imad last updated on 30/Jan/18

prove that (π/(4cos(((πα)/2))))=Σ_(p=0) ^∞ (((2p+1)(−1)^p )/((2p+1)^2 −α^2 )) α ∈R−Z.

p r o v e t h a t \frac{π}{4 c o s (\frac{π α}{2})} = \sum_{p = 0}^{\infty} \frac{(2 p + 1) {(- 1)}^{p}}{{(2 p + 1)}^{2} - α^{2}}

α \in R - Z .

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