Some new formulas for pi
(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:
https://lup.lub.lu.se/record/279869
- author
- Almkvist, Gert LU ; Krattenthaler, C and Petersson, Joakim LU
- organization
- publishing date
- 2003
- 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
- external identifiers
-
- wos:000221167000006
- scopus:2442621411
- 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
- 2016-04-01 12:29:41
- date last changed
- 2022-04-13 19:44:22
@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}},
keywords = {{Fast converging series for pi; determinant evaluations}},
language = {{eng}},
number = {{4}},
pages = {{441--456}},
publisher = {{A K Peters}},
series = {{Experimental Mathematics}},
title = {{Some new formulas for pi}},
url = {{http://www.expmath.org/expmath/volumes/12/12.4/Almkvist.pdf}},
volume = {{12}},
year = {{2003}},
}