A family of shifted harmonic sums

被引：41
|
作者：
Sofo, Anthony [1 ]
Srivastava, H. M. [2 ]
机构：
[1] Victoria Univ Technol, Sect Math, VU Coll, Melbourne, Vic 8001, Australia
[2] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
来源：
RAMANUJAN JOURNAL | 2015年 / 37卷 / 01期
关键词：
Harmonic numbers; Riemann Zeta function; Integral representations; Binomial coefficients; Euler sums; Psi (or Digamma) function; Polygamma functions; SUMMATION FORMULAS; NUMBER SUMS; SERIES;
D O I：
10.1007/s11139-014-9600-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we first develop a set of identities for Euler-type sums. We then investigate products of the shifted harmonic numbers and the reciprocal binomial coefficients. We briefly indicate relevant connections of the results presented here with those given by earlier authors. As by-products of our investigation, we derive several (presumably new) one-parameter and two-parameter summation formulas for the hypergeometric series at argument 1.
引用
收藏
页码：89 / 108
页数：20
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