English

Summation formulas of hyperharmonic numbers with their generalizations II

Number Theory 2021-03-22 v1 Combinatorics

Abstract

In 1990, Spie\ss \, gave some identities of harmonic numbers including the types of =1nkH\sum_{\ell=1}^n\ell^k H_\ell, =1nkHn\sum_{\ell=1}^n\ell^k H_{n-\ell} and =1nkHHn\sum_{\ell=1}^n\ell^k H_\ell H_{n-\ell}. In this paper, we derive several formulas of hyperharmonic numbers including =0nph(r)hn(s)\sum_{\ell=0}^{n} {\ell}^{p} h_{\ell}^{(r)} h_{n-\ell}^{(s)} and =0np(h(r))2\sum_{\ell=0}^n \ell^{p}(h_{\ell}^{(r)})^{2}. Some more formulas of generalized hyperharmonic numbers are also shown.

Keywords

Cite

@article{arxiv.2103.10658,
  title  = {Summation formulas of hyperharmonic numbers with their generalizations II},
  author = {Takao Komatsu and Rusen Li},
  journal= {arXiv preprint arXiv:2103.10658},
  year   = {2021}
}

Comments

27 pages

R2 v1 2026-06-24T00:20:40.598Z