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2020 | OriginalPaper | Chapter

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

Author : Jakob Ablinger

Published in: Mathematical Aspects of Computer and Information Sciences

Publisher: Springer International Publishing

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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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previous chapter Evaluation of Chebyshev Polynomials on Intervals and Application to Root Finding

next chapter Generalized Integral Dependence Relations

The package HarmonicSums (Version 1.0 19/08/19) together with a Mathematica notebook containing the computations described here can be downloaded at https://risc.jku.at/sw/harmonicsums.

The Mathematica built-in differential equation solver was not sufficient to solve these differential equations. The implemented solver does not rely on the Mathematica built-in DSolve.

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Title: Proving Two Conjectural Series for and Discovering More Series for
Author: Jakob Ablinger
Publisher: Springer International Publishing
Book: Mathematical Aspects of Computer and Information Sciences
Print ISBN: 978-3-030-43119-8

Electronic ISBN: 978-3-030-43120-4

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-43120-4_5

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