N ov 2 00 1 SOME NEW FORMULAS FOR π

Abstract

We show how to find series expansions for π of the form π = ∞ n=0 S(n) 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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Cite this paper

@inproceedings{Almkvist2001NO2, title={N ov 2 00 1 SOME NEW FORMULAS FOR π}, author={Gert Almkvist and Christian Krattenthaler}, year={2001} }