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arXiv · 2411.11849

New harmonic number series

Kunle Adegoke·Robert Frontczak
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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.

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Kunle Adegoke, Robert Frontczak. 2024-10-31. New harmonic number series. https://arxiv.org/abs/2411.11849

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