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_
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