Euler sums of generalized harmonic numbers and connected extensions

Can M., Kargın L., Dil A., Soylu G.

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, cilt.17, sa.2, ss.401-417, 2023 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.2298/aadm210122014c
  • Dergi Adı: APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.401-417
  • Akdeniz Üniversitesi Adresli: Evet

Özet

This paper presents the evaluation of the Euler sums of generalized hyperharmonic numbers H(p,q)n ζH(p,q)(r) = ∞Xn=1 H(p,q)n/nr in terms of the famous Euler sums of generalized harmonic numbers. Moreover, several infinite series, whose terms consist of certain harmonic numbers and reciprocal binomial coefficients, are evaluated in terms of the Riemann zeta values.