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

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.

Citation
Zhu, T. (2022). Explicit expressions for some linear Euler-type sums containing harmonic and skew-harmonic numbers. Journal of Classical Analysis, 2, 79–101. https://doi.org/10.7153/jca-2022-20-07

Publisher
Element d.o.o.

Journal
Journal of Classical Analysis

DOI
10.7153/jca-2022-20-07

Additional Links
http://jca.ele-math.com/20-07

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