On Evaluations of Euler-Type Sums of Hyperharmonic Numbers


Kargın L., Can M., Dil A., Cenkci M.

Bulletin of the Malaysian Mathematical Sciences Society, vol.45, no.1, pp.113-131, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.1007/s40840-021-01179-8
  • Journal Name: Bulletin of the Malaysian Mathematical Sciences Society
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.113-131
  • Keywords: Euler sums, Harmonic numbers, Hyperharmonic numbers, Binomial coefficients, Stirling numbers, Riemann zeta values, HARMONIC SUMS, SERIES
  • Akdeniz University Affiliated: Yes

Abstract

© 2021, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.We give explicit evaluations of the linear and non-linear Euler sums of hyperharmonic numbers hn(r) with reciprocal binomial coefficients. These evaluations enable us to extend closed form formula of Euler sums of hyperharmonic numbers to an arbitrary integer r. Moreover, we reach at explicit formulas for the shifted Euler-type sums of harmonic and hyperharmonic numbers. All the evaluations are provided in terms of the Riemann zeta values, harmonic numbers and linear Euler sums.