English

Euler sums of generalized harmonic numbers and connected extensions

Number Theory 2021-03-18 v3

Abstract

This paper presents the evaluation of the Euler sums of generalized hyperharmonic numbers Hn(p,q)H_{n}^{\left( p,q\right) } ζH(p,q)(r)=n=1Hn(p,q)nr \zeta_{H^{\left( p,q\right) }}\left( r\right) =\sum\limits_{n=1}^{\infty }\dfrac{H_{n}^{\left( p,q\right) }}{n^{r}}% 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 Riemann zeta values.

Keywords

Cite

@article{arxiv.2006.00620,
  title  = {Euler sums of generalized harmonic numbers and connected extensions},
  author = {Mümün Can and Levent Kargın and Ayhan Dil and Gültekin Soylu},
  journal= {arXiv preprint arXiv:2006.00620},
  year   = {2021}
}
R2 v1 2026-06-23T15:56:49.608Z