A single parameter Hermite-Pad 'e series representations for Ap 'ery's\n constant

2018/06/15 by Anier Soria-Lorente, Soria-Lorente, Anier, Stefan Berres +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1806.05988

openalex publication_date 2018/06/15 · openalex created_date 2021/03/15 · openalex updated_date 2026/07/28

Abstract

Inspired by the results of Rhin and Viola (2001), the purpose of this work is\nto elaborate on a series representation for \ζ \( 3\) which only\ndepends on one single integer parameter. This is accomplished by deducing a\nHermite-Pad 'e approximation problem using ideas of Sorokin (1998). As a\nconsequence we get a new recurrence relation for the approximation of\n\ζ(3) as well as a corresponding new continued fraction expansion for\n\ζ(3), which do no reproduce Ap 'ery's phenomenon, i.e., though the\napproaches are different, they lead to the same sequence of diophantine\napproximations to \ζ \( 3\) . Finally, the convergence rates of\nseveral series representations of \ζ(3) are compared.\n

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