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2003 Some New Formulas for 𝜋
Gert Almkvist, Christian Krattenthaler, Joakim Petersson
Experiment. Math. 12(4): 441-456 (2003).

Abstract

We show how to find series expansions for {\small $\pi$} of the form {\small $\pi=\sum_{n=0}^\infty {S(n)}\big/{\binom{mn}{pn}a^n}$}, where {\small $S(n)$} is some polynomial in n (depending on m, p, a). We prove that there exist such expansions for {\small $m=8k$, $p=4k$, $a=(-4)^k$}, for any k, and give explicit examples for such expansions for small values of m, p, a and a.

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Gert Almkvist. Christian Krattenthaler. Joakim Petersson. "Some New Formulas for 𝜋." Experiment. Math. 12 (4) 441 - 456, 2003.

Information

Published: 2003
First available in Project Euclid: 18 June 2004

zbMATH: 1161.11419
MathSciNet: MR2043994

Subjects:
Primary: 11Y60
Secondary: 15A15

Keywords: determinant evaluations , Fast converging series for Pi

Rights: Copyright © 2003 A K Peters, Ltd.

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Vol.12 • No. 4 • 2003
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