Evaluating Infinite Series Involving Harmonic Numbers by Integration

被引：2
|
作者：
Li, Chunli [1 ]
Chu, Wenchang [1 ]
机构：
[1] Zhoukou Normal Univ, Sch Math & Stat, Zhuokou 466001, Peoples R China
来源：
MATHEMATICS | 2024年 / 12卷 / 04期
关键词：
Euler sum; harmonic number; trilogarithm; Catalan's constant; Riemann zeta function;
D O I：
10.3390/math12040589
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页数：21
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