Proving two conjectural series for ζ(7) and discovering more series for ζ(7)

2019/08/19 by Jakob Ablinger, Ablinger, Jakob
Mathematics · Medicine · #Advanced Mathematical Identities #Analytic Number Theory Research #Berberine and alkaloids research #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Symbolic Computation (cs.SC)

paper · pdf · doi:10.48550/arxiv.1908.06631

openalex publication_date 2019/08/19 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We give a proof of two identities involving binomial sums at infinity conjectured by Z-W Sun. In order to prove these identities, we use a recently presented method i.e. we view the series as specializations of generating series and derive integral representations. Using substitutions, we express these integral representations in terms of cyclotomic harmonic polylogarithms. Finally, by applying known relations among the cyclotomic harmonic polylogarithms, we derive the results. These methods are implemented in the computer algebra package HarmonicSums.

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