Experimental Mathematics

Simultaneous Generation of Koecher and Almkvist-Granville's Apéry-Like Formulae

T. Rivoal

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Abstract

We prove a very general identity, conjectured by Henri Cohen, involving the generating function of the family {\small $(\zeta(2r+4s+3))_{r,s\ge 0}$}: it unifies two identities, proved by Koecher in 1980 and Almkvist and Granville in 1999, for the generating functions of {\small $(\zeta(2r+3))_{r\ge 0}$} and {\small $(\zeta(4s+3))_{s\ge 0}$}, respectively. As a consequence, we obtain that, for any integer {\small $j \ge 0$}, there exists at least {\small $[j/2]+1$ } Apéry-like formulae for {\small $\zeta(2j+3)$}.

Article information

Source
Experiment. Math., Volume 13, Issue 4 (2004), 503-508.

Dates
First available in Project Euclid: 22 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.em/1109106442

Mathematical Reviews number (MathSciNet)
MR2118275

Zentralblatt MATH identifier
1127.11057

Subjects
Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$
Secondary: 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 11J72: Irrationality; linear independence over a field

Keywords
Riemann zeta function Apéry-like series generating functions

Citation

Rivoal, T. Simultaneous Generation of Koecher and Almkvist-Granville's Apéry-Like Formulae. Experiment. Math. 13 (2004), no. 4, 503--508. https://projecteuclid.org/euclid.em/1109106442


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