This material has been published in Experiment. Math. 12 (2003), 441-456, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by A. K. Peters. This material may not be copied or reposted without explicit permission.

Gert Almkvist, Christian Krattenthaler and Joakim Petersson

Some new formulas for pi

(28 pages)

Abstract. We show how to find arbitrarily fast convergent series expansions for \pi of the form \pi=\sum_{n=0}^\infty {S(n)}\big/{\binom{mn}{pn}a^n}, where S(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.

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