Evaluating Infinite Series Involving Harmonic Numbers by Integration-Reference-Cited by-同舟云学术

Evaluating Infinite Series Involving Harmonic Numbers by Integration

Published:2024-02-16 Issue:4 Volume:12 Page:589
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Li Chunli¹^ORCID,Chu Wenchang¹^ORCID

Affiliation:

1. School of Mathematics and Statistics, Zhoukou Normal University, Zhuokou 466001, China

Abstract

Eight infinite series involving harmonic-like numbers are coherently and systematically reviewed. They are evaluated in closed form exclusively by integration together with calculus and complex analysis. In particular, a mysterious series W is introduced and shown to be expressible in terms of the trilogarithm function. Several remarkable integral values and difficult infinite series identities are shown as consequences.

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/4/589/pdf

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