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Some new formulas for pi

Almkvist, Gert LU ; Krattenthaler, C and Petersson, Joakim LU (2003) In Experimental Mathematics 12(4). p.441-456
Abstract
We show how to find series expansions for pi of the form pi = Sigma(n=0)(infinity) S(n)/((mn)(pn)) a(n), is some polynomial in n (depending on m,p,a). We prove that there exist such expansions for m = 8k, p = 4k, a = (-4)(k), for any k, and give explicit examples for such expansions for small values of m, p and a.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Fast converging series for pi, determinant evaluations
in
Experimental Mathematics
volume
12
issue
4
pages
441 - 456
publisher
A K Peters LTD
external identifiers
  • wos:000221167000006
ISSN
1944-950X
language
English
LU publication?
yes
id
8c189872-a594-492b-9735-700326239f70 (old id 279869)
alternative location
http://www.expmath.org/expmath/volumes/12/12.4/Almkvist.pdf
date added to LUP
2007-08-22 10:04:07
date last changed
2016-04-15 20:31:11
@article{8c189872-a594-492b-9735-700326239f70,
  abstract     = {We show how to find series expansions for pi of the form pi = Sigma(n=0)(infinity) S(n)/((mn)(pn)) a(n), is some polynomial in n (depending on m,p,a). We prove that there exist such expansions for m = 8k, p = 4k, a = (-4)(k), for any k, and give explicit examples for such expansions for small values of m, p and a.},
  author       = {Almkvist, Gert and Krattenthaler, C and Petersson, Joakim},
  issn         = {1944-950X},
  keyword      = {Fast converging series for pi,determinant evaluations},
  language     = {eng},
  number       = {4},
  pages        = {441--456},
  publisher    = {A K Peters LTD},
  series       = {Experimental Mathematics},
  title        = {Some new formulas for pi},
  volume       = {12},
  year         = {2003},
}