Hyperharmonic series involving Hurwitz zeta function

Mezö I., DİL A.

JOURNAL OF NUMBER THEORY, vol.130, no.2, pp.360-369, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 130 Issue: 2
  • Publication Date: 2010
  • Doi Number: 10.1016/j.jnt.2009.08.005
  • Journal Name: JOURNAL OF NUMBER THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.360-369
  • Keywords: Hyperharmonic numbers, Euler sums, Riemann zeta function, Hurwitz zeta function, Hypergeometric series, STIRLING NUMBERS
  • Akdeniz University Affiliated: Yes

Abstract

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.