Timeline for Exact formula for $\sum_{n=0}^{+\infty}\frac1{n^2+1}$

10 events

when toggle format	what		by	license	comment
Nov 26, 2022 at 21:37	history	edited	Todd Trimble	CC BY-SA 4.0	cot --> coth
Dec 1, 2015 at 12:07	comment	added	Fedor Petrov		oh, I did not know this trick with polynomial
Dec 1, 2015 at 11:32	comment	added	Pietro Majer		(no: I've just found Herglotz trick on line)
Dec 1, 2015 at 11:24	comment	added	Pietro Majer		Just to complete the picture, the expansion of the cotangent can be obtained by logarithmic differentiation from the infinite product for $\sin(\pi x)$, and the infinite product for $\sin(\pi x)$ can be obtained as dominated limit on the (easily computed) complete factorization of the polynomials $(1+iz/n)^n-(1-iz/n)^n$, that converge to $e^{iz}-e^{-iz}=2i\sin(z)$ (Is this Herglotz' proof?)
Dec 1, 2015 at 7:48	history	edited	Fedor Petrov	CC BY-SA 3.0	added 965 characters in body
Dec 1, 2015 at 5:59	comment	added	Fedor Petrov		Indeed, but this works for all rational functions.
Dec 1, 2015 at 0:14	comment	added	Alexandre Eremenko		Yes, but he asked to sum $f(n)$ with a more general class of functions $f$.
S Nov 30, 2015 at 22:52	history	suggested	CommunityBot	CC BY-SA 3.0	Corrected two typos.
Nov 30, 2015 at 22:45	review	Suggested edits
S Nov 30, 2015 at 22:52
Nov 30, 2015 at 21:58	history	answered	Fedor Petrov	CC BY-SA 3.0