Euler sums of generalized harmonic numbers and connected extensions

Can M., Kargın L., Dil A., Soylu G.

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, vol.17, no.2, pp.401-417, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.2298/aadm210122014c
  • Journal Name: APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.401-417
  • Akdeniz University Affiliated: Yes

Abstract

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.