From: Robin Chapman Subject: Re: summation methods Date: Mon, 07 Jun 1999 13:14:10 GMT Newsgroups: sci.math Keywords: Poisson's summation formula In article <7jgc33\$lp1\$1@nnrp1.deja.com>, Serge Zlobin wrote: > In a certain article I've read that the infinite sum (-1)^n/(n^2+1) can > be evaluate through Poisson's summation formula or Mittag-Leffler > expansions of trigonometric functions. Can someone explain what these > methods are? Poisson summation: sum_{n=-infinfy}^infinity f(n) = sum_{m=-infinfy}^infinity F(m) where F is the Fourier transform of f: F(t) = integral_{-infinity}^infinity exp(- 2 pi i xt) f(x) dx, provided that f satisfies some mild analytic conditions: for instance that it be differentiable and it and its derivative decay resonably rapidly at infinity. -- Robin Chapman http://www.maths.ex.ac.uk/~rjc/rjc.html "They did not have proper palms at home in Exeter." Peter Carey, _Oscar and Lucinda_ Sent via Deja.com http://www.deja.com/ Share what you know. Learn what you don't.