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Summation formulas of hyperharmonic numbers with their generalizations II

Published 19 Mar 2021 in math.NT and math.CO | (2103.10658v1)

Abstract: In 1990, Spie\ss \, gave some identities of harmonic numbers including the types of $\sum_{\ell=1}n\ellk H_\ell$, $\sum_{\ell=1}n\ellk H_{n-\ell}$ and $\sum_{\ell=1}n\ellk H_\ell H_{n-\ell}$. 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.

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