New harmonic number series
Number Theory
2024-11-20 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.
Cite
@article{arxiv.2411.11849,
title = {New harmonic number series},
author = {Kunle Adegoke and Robert Frontczak},
journal= {arXiv preprint arXiv:2411.11849},
year = {2024}
}