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Matematicheskie Zametki, 2007, Volume 81, Issue 2, Pages 226–239
DOI: https://doi.org/10.4213/mzm3550 (Mi mzm3550) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Rhin Integrals

S. A. Zlobin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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DOI: https://doi.org/10.4213/mzm3550
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.
Received: 19.12.2005
Revised: 10.06.2006
English version:
Mathematical Notes, 2007, Volume 81, Issue 2, Pages 201–212
DOI: https://doi.org/10.1134/S0001434607010233
Bibliographic databases:
UDC: 511.3
Language: Russian
Citation: S. A. Zlobin, “Rhin Integrals”, Mat. Zametki, 81:2 (2007), 226–239; Math. Notes, 81:2 (2007), 201–212
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    		Математические заметки Mathematical Notes
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