Well-poised generation of Apéry-like recursions

Title: Well-poised generation of Apéry-like recursions
Creator: Zudilin, W.
Relation: Journal of Computational and Applied Mathematics Vol. 178, Issue 1-2, p. 513-521
Publisher Link: http://dx.doi.org/10.1016/j.cam.2003.11.016
Publisher: Elsevier
Resource Type: journal article
Date: 2005
Description: The idea to use classical hypergeometric series and, in particular, well-poised hypergeometric series in diophantine problems of the values of the polylogarithms has led to several novelties in number theory and neighbouring areas of mathematics. Here, we present a systematic approach to derive second-order polynomial recursions for approximations to some values of the Lerch zeta function, depending on the fixed (but not necessarily real) parameter α satisfying the condition Re(α)<1. Substituting α=0 into the resulting recurrence equations produces the famous recursions for rational approximations to ζ(2), ζ(3) due to Apéry, as well as the known recursion for rational approximations to ζ(4). Multiple integral representations for solutions of the constructed recurrences are also given.
Subject: hypergeometric series; polynomial recursion; Apéry's approximations; zeta value; multiple integral
Identifier: http://hdl.handle.net/1959.13/934874
Identifier: uon:11925
Identifier: ISSN:0377-0427
Language: eng
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