English

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.

Keywords

Cite

@article{arxiv.2411.11849,
  title  = {New harmonic number series},
  author = {Kunle Adegoke and Robert Frontczak},
  journal= {arXiv preprint arXiv:2411.11849},
  year   = {2024}
}
R2 v1 2026-06-28T20:03:58.174Z