Evaluation of Euler-like sums via Hurwitz zeta values

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DİL A., Mezo I., CENKCİ M.

TURKISH JOURNAL OF MATHEMATICS, cilt.41, sa.6, ss.1640-1655, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 6
  • Basım Tarihi: 2017
  • Doi Numarası: 10.3906/mat-1603-4
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1640-1655
  • Anahtar Kelimeler: Harmonic numbers, hyperharmonic numbers, generalized harmonic numbers, Euler sums, multiple zeta functions, Riemann zeta function, Hurwitz zeta function, HYPERHARMONIC NUMBERS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper we collect two generalizations of harmonic numbers (namely generalized harmonic numbers and hyperharmonic numbers) under one roof. Recursion relations, closed-form evaluations, and generating functions of this unified extension are obtained. In light of this notion we evaluate some particular values of Euler sums in terms of odd zeta values. We also consider the noninteger property and some arithmetical aspects of this unified extension.