Empirically determined Apéry-like formulae for ζ(4n+3)

Title: Empirically determined Apéry-like formulae for ζ(4n+3)
Creator: Borwein, Jonathan; Bradley, David
Relation: Experimental Mathematics Vol. 6, Issue 3, p. 181-194
Publisher Link: http://dx.doi.org/10.1080/10586458.1997.10504608
Publisher: A. K. Peters
Resource Type: journal article
Date: 1997
Description: Some rapidly convergent formulae for special values of the Riemann zeta function are given. We obtain a generating function formula for ζ(4n+3) that generalizes Apéry's series for ζ(3), and appears to give the best possible series relations of this type, at least for n < 12. The formula reduces to a finite but apparently nontrivial combinatorial identity. The identity is equivalent to an interesting new integral evaluation for the central binomial coefficient. We outline a new technique for transforming and summing certain infinite series. We also derive a formula that provides strange evaluations of a large new class of nonterminating hypergeometric series.
Subject: Apéry's series; Apéry-like formulae; formulae; Riemann zeta function
Identifier: http://hdl.handle.net/1959.13/940789
Identifier: uon:13102
Identifier: ISSN:1058-6458
Language: eng
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