Summation formulas of hyperharmonic numbers with their generalizations II

Abstract

In 1990, Spieß\, gave some identities of harmonic numbers including the types of ${\sum }_{\ell =1}^n{\ell }^k{H}_{\ell }$, ${\sum }_{\ell =1}^n{\ell }^k{H}_{n-\ell }$ and ${\sum }_{\ell =1}^n{\ell }^k{H}_{\ell }{H}_{n-\ell }$. In this paper, we derive several formulas of hyperharmonic numbers including ${\sum }_{\ell =0}^n{\ell }^p{h}_{\ell }^{(r)}{h}_{n-\ell }^{(s)}$ and ${\sum }_{\ell =0}^n{\ell }^p(h_{\ell }^{(r)}{)}^2$. Some more formulas of generalized hyperharmonic numbers are also shown.

27 pages