On Zudilin-like rational approximations to ζ (5)

Anier Soria Lorente
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 2, Pages 104—116
DOI: 10.7546/nntdm.2018.24.2.104-116
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Authors and affiliations

Anier Soria Lorente
Department of Mathematics, University of Granma
Bayamo, Granma, Cuba

Abstract

In this paper we obtain two Zudilin-Like recurrence relations of third order for ζ (5), after applying Zeilberger’s algorithm of creative telescoping to some hypergeometric series. These recurrence relations do not supply diophantine approximations to ζ (5) that prove its irrationality, however it presents an algorithm for fast calculation of this constant. Moreover, we deduce a new continued fraction expansion for ζ (5) as a consequence.

Keywords

  • Riemann zeta function
  • Recurrence relation
  • Continued fraction expansion
  • Irrationality

2010 Mathematics Subject Classification

  • Primary: 11B37, 30B70, 14G10, 11J72, 11M06
  • Secondary: 37B20, 11A55, 11J70, 11Y55, 11Y65

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Cite this paper

APA

Soria Lorente, A. (2018). On Zudilin-like rational approximations to ζ(5). Notes on Number Theory and Discrete Mathematics, 24(2), 104-116, doi: 10.7546/nntdm.2018.24.2.104-116.

Chicago

Soria Lorente, Anier. “On Zudilin-like Rational Approximations to ζ(5).” Notes on Number Theory and Discrete Mathematics 24, no. 2 (2018): 104-116, doi: 10.7546/nntdm.2018.24.2.104-116.

MLA

Soria Lorente, Anier. “On Zudilin-like Rational Approximations to ζ(5).” Notes on Number Theory and Discrete Mathematics 24.2 (2018): 104-116. Print, doi: 10.7546/nntdm.2018.24.2.104-116.

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