EXPLICIT EXPRESSIONS FOR SOME LINEAR EULER–TYPE SUMS CONTAINING HARMONIC AND SKEW–HARMONIC NUMBERS

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Abstract

Closed-form expressions for the three general linear Euler-type sums containing the harmonic numbers Hn and the skew-harmonic numbers Hn ∞ ∑ n=1 (−1)nHn (2n+1)2q+1 , ∞ ∑ n=1 Hn (2n+1)q , and ∞ ∑ n=1 (−1)nHn (2n+1)2q+1 , where q is a positive integer greater than or equal to zero or two as needed to ensure convergence are given. Closed-form expressions for several other closely related generalised logarithmic integrals and sums are also presented.
Original languageEnglish (US)
Pages (from-to)79-101
Number of pages23
JournalJournal of Classical Analysis
Volume20
Issue number2
DOIs
StatePublished - 2022

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