Approximations to -, di- and tri-logarithms

doi:10.1016/j.cam.2005.04.076

Journal of Computational and Applied Mathematics

Volume 202, Issue 2, 15 May 2007, Pages 450-459

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Abstract

We propose hypergeometric constructions of simultaneous approximations to polylogarithms. These approximations suit for computing the values of polylogarithms and satisfy 4-term Apéry-like (polynomial) recursions.

MSC

33C20

33F10

11J70

11M06

Keywords

Dilogarithm

Trilogarithm

Zeta value

Hypergeometric series

Algorithm of creative telescoping

Polynomial recursion

Apéry's approximations