This article is cited in 1 paper

Rhin Integrals

S. A. Zlobin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We study a generalization of the integrals examined by G. Rhin, in the form of multiple integrals. These integrals yield rational approximations to the values of the Riemann zeta function. In a particular case, we obtain Apéry approximations used to prove the irrationality of the number $\zeta(3)$.

Keywords: Rhin integral, Riemann zeta function, multiple integral, Apéry approximation, polylogarithm, Beukers integral, hypergeometric function.

UDC: 511.3

Received: 19.12.2005
Revised: 10.06.2006

DOI: 10.4213/mzm3550

 English version: Mathematical Notes, 2007, 81:2, 201–212

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