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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
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
Citation:
S. A. Zlobin, “Rhin Integrals”, Mat. Zametki, 81:2 (2007), 226–239; Math. Notes, 81:2 (2007), 201–212
Linking options:
https://www.mathnet.ru/eng/mzm3550https://doi.org/10.4213/mzm3550 https://www.mathnet.ru/eng/mzm/v81/i2/p226
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Abstract page: | 426 | Full-text PDF : | 227 | References: | 77 | First page: | 2 |
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