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This version is not peer-reviewed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
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment