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Mat. Zametki, 2007, Volume 81, Issue 2, Pages 226–239 (Mi mz3550)  

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

DOI: https://doi.org/10.4213/mzm3550

Full text: PDF file (449 kB)
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English version:
Mathematical Notes, 2007, 81:2, 201–212

Bibliographic databases:

UDC: 511.3
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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. W. Zudilin, “Arithmetic hypergeometric series”, Russian Math. Surveys, 66:2 (2011), 369–420  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математические заметки Mathematical Notes
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