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Proving Two Conjectural Series for \(\zeta (7)\) and Discovering More Series for \(\zeta (7)\)

  • Jakob AblingerEmail author
Conference paper
  • 19 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11989)

Abstract

We give a proof of two identities involving binomial sums at infinity conjectured by Zhi-Wei 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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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Research Institute for Symbolic ComputationJohannes Kepler UniversityLinzAustria

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