Hyperharmonic series involving Hurwitz zeta function

Mezö I., DİL A.

JOURNAL OF NUMBER THEORY, cilt.130, sa.2, ss.360-369, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 130 Sayı: 2
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1016/j.jnt.2009.08.005
  • Dergi Adı: JOURNAL OF NUMBER THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.360-369
  • Anahtar Kelimeler: Hyperharmonic numbers, Euler sums, Riemann zeta function, Hurwitz zeta function, Hypergeometric series, STIRLING NUMBERS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.