On new rational approximants to ζ(3)

2012/04/30 by J. Arvesú, Arvesú, J., Anier Soria-Lorente +1
Mathematics · #11A55 #11B37 #11J70 #11J72 #11M06 (Primary) 30B70 #33C47 (Secondary) #42C05 #Advanced Mathematical Identities #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #History and Overview (math.HO) #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1204.6712

openalex publication_date 2012/04/30 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

New (infinitely many) rational approximants to ζ(3) proving its irrationality are given. The recurrence relations for the numerator and denominator of these approximants as well as their continued fraction expansions are obtained. A comparison of our approximants with Apéry's approximants to ζ(3) is shown.

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