Evaluating Infinite Series Involving Harmonic Numbers by Integration

Chunli Li () and Wenchang Chu ()
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Chunli Li: School of Mathematics and Statistics, Zhoukou Normal University, Zhuokou 466001, China
Wenchang Chu: School of Mathematics and Statistics, Zhoukou Normal University, Zhuokou 466001, China

Mathematics, 2024, vol. 12, issue 4, 1-21

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.

Keywords: Euler sum; harmonic number; trilogarithm; Catalan’s constant; Riemann zeta function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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