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
Full paper (PDF, 209 Kb)

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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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