Hyperharmonic series involving Hurwitz zeta function

JOURNAL OF NUMBER THEORY

卷:130

Article

Mezo, Istvan¹  Dil, Ayhan² 

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

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

关键词: Hyperharmonic numbers;    Euler sums;    Riemann zeta function;    Hurwitz zeta function;    Hypergeometric series;   

DOI  :  10.1016/j.jnt.2009.08.005

来源: Elsevier

【 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.

【 授权许可】

Free