Abstract
In 1990, Spieß gave some identities of harmonic numbers including the types \(\sum _{\ell =1}^n\ell ^k H_\ell \), \(\sum _{\ell =1}^n\ell ^k H_{n-\ell }\) 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 \(\sum _{\ell =0}^n \ell ^{p}\left( h_{\ell }^{(r)}\right) ^{2}\). Some more formulas of generalized hyperharmonic numbers are also shown.
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The data that support the findings of this study are available from the corresponding author upon reasonable request.
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The authors are grateful to the anonymous referee for helpful comments.
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Komatsu, T., Li, R. Summation formulas of hyperharmonic numbers with their generalizations. Afr. Mat. 34, 81 (2023). https://doi.org/10.1007/s13370-023-01131-y
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DOI: https://doi.org/10.1007/s13370-023-01131-y