A simple approximate expression for the Apéry's constant accurate to 21 digits

Details A simple approximate expression for the Apéry's constant accurate to 21 digits A simple approximate expression for the Apéry's constant accurate to 21 digits

2009-10-14

arxiv.org/abs/0910.2684v3

Mathematics

Number Theory

11 pages, no figures. Revised version (Submitted to: Exp. Mathematics) (04/08/2011)

Scientific paper

In this note, I present a simple approximate expression for the number $\zeta{(3)}$, known as the Ap\'{e}ry's constant, which is accurate to 21 digits. This finite closed-form expression has been found experimentally via the PSLQ algorithm, with a suitable search basis involving the numbers $\,\pi$, $\,\ln{2}\,$, $\,\ln{(1+\sqrt{2}\,)}$, and $G$ (the Catalan's constant). The short \emph{Maple} code written for finding the rational coefficients is also shown.

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