Some fast convergent series for the mathematical constants ζ(4) and ζ(5)

2023/03/14 by Chuanan Wei, Wei, Chuanan
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2303.07887

openalex publication_date 2023/03/14 · openalex created_date 2023/03/17 · openalex updated_date 2026/07/28

Abstract

Recently, Sun [preprint, arXiv: 2210.07238v7] proposed two conjectural series for the mathematical constant ζ(4) and two conjectural series for the mathematical constant ζ(5). In terms of the operator method and two hypergeometric transformations, we prove these four conjectures. Furthermore, we also find some new series for the two constants in this paper.

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