Hyperharmonic series involving Hurwitz zeta function

被引：41

作者：

Mezo, Istvan ^{[1
]}

Dil, Ayhan ^{[2
]}

机构：

[1] Univ Debrecen, Inst Math, Debrecen, Hungary

[2] Akdeniz Univ, Dept Math, Fac Art & Sci, TR-07058 Antalya, Turkey

来源：

JOURNAL OF NUMBER THEORY | 2010年 / 130卷 / 02期

关键词：

Hyperharmonic numbers; Euler sums; Riemann zeta function; Hurwitz zeta function; Hypergeometric series; STIRLING NUMBERS;

D O I：

10.1016/j.jnt.2009.08.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the sum of the series formed by the so-called hyperharmonic numbers can be expressed in terms of the Riemann zeta function. These results enable us to reformulate Euler's formula involving the Hurwitz zeta function. In additon, we improve Conway and Guy's formula for hyperharmonic numbers. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：360 / 369

页数：10

共 9 条

[1]

[Anonymous], BOOK NUMBERS

[2]

Benjamin A.T., 2003, Integers, V3, P1

[3] ON AN INTRIGUING INTEGRAL AND SOME SERIES RELATED TO ZETA(4) [J].