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2004 Simultaneous Generation of Koecher and Almkvist-Granville's Apéry-Like Formulae
T. Rivoal
Experiment. Math. 13(4): 503-508 (2004).

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 $\zeta(2j+3)$}.

Citation

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T. Rivoal. "Simultaneous Generation of Koecher and Almkvist-Granville's Apéry-Like Formulae." Experiment. Math. 13 (4) 503 - 508, 2004.

Information

Published: 2004
First available in Project Euclid: 22 February 2005

zbMATH: 1127.11057
MathSciNet: MR2118275

Subjects:
Primary: 11M06
Secondary: 05A15 , 11J72

Keywords: Apéry-like series , generating functions , Riemann zeta function

Rights: Copyright © 2004 A K Peters, Ltd.

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Vol.13 • No. 4 • 2004
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