Preprint Article Version 1 This version is not peer-reviewed

New Harmonic Number Series

Version 1 : Received: 4 November 2024 / Approved: 5 November 2024 / Online: 6 November 2024 (08:43:03 CET)

How to cite: Adegoke, K.; Frontczak, R. New Harmonic Number Series. Preprints 2024, 2024110288. https://doi.org/10.20944/preprints202411.0288.v1 Adegoke, K.; Frontczak, R. New Harmonic Number Series. Preprints 2024, 2024110288. https://doi.org/10.20944/preprints202411.0288.v1

Abstract

Based on a recent representation of the psi function due to Guillera and Sondow and independently Boyadzhiev, new closed forms for various series involving harmonic numbers and inverse factorials are derived. A high point of the presentation is the rediscovery, by much simpler means, of a famous quadratic Euler sum originally discovered in 1995 by Borwein and Borwein.

Keywords

harmonic number; Riemann zeta function; binomial coefficient; Euler sum

Subject

Computer Science and Mathematics, Discrete Mathematics and Combinatorics

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