Integral representations for ζ(3) with the inverse sine function

2021/08/03 by Masato Kobayashi, Kobayashi, Masato
Mathematics · #2020 Primary:11M06 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Secondary:11M41 #math.NT #msc:2020

paper · pdf · doi:10.48550/arxiv.2108.01247

9 pages

arxiv created 2021/08/03 · openalex publication_date 2021/08/03 · arxiv updated 2021/08/04 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We show four new integral representations for ζ(3) as a reformulation of Ewell (1990) and Yue-Williams (1993) with the inverse sine function and Wallis integral. As a consequence, we also show a local integral representation for the trilogarithm function.

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