prove-that-picotan-pi-1-n-1-2-2-n-2-with-R-Z-prove-also-that-for-t-0-cotan-t-1-t-n-1-2t-t-2-n-2-pi-2-

Question Number 68129 by mathmax by abdo last updated on 05/Sep/19

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

w i t h α \in R - Z .

p r o v e a l s o t h a t f o r t \neq 0

c o t a n (t) = \frac{1}{t} + \sum_{n = 1}^{\infty} \frac{2 t}{t^{2} - n^{2} π^{2}}