EXPLICIT EVALUATION OF HARMONIC SUMS

被引：2
|
作者：
Xu, Ce [1 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
来源：
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY | 2018年 / 33卷 / 01期
关键词：
harmonic number; Euler sum; Riemann zeta function; Stirling number;
D O I：
10.4134/CKMS.c160277
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several quadratic and cubic Euler sums through zeta values and linear sums. Furthermore, some relationships between harmonic numbers and Stirling numbers of the first kind are established.
引用
收藏
页码：13 / 36
页数：24
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