The method of residue and identities on harmonic numbers

Huanhuan Zheng; Haitao Jin

doi:10.1117/12.2627789

22 April 2022 The method of residue and identities on harmonic numbers

Huanhuan Zheng, Haitao Jin

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 1216333 (2022) https://doi.org/10.1117/12.2627789
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

By using the method of residue, we give a hypergeometric representation for the generalized harmonic numbers. Then the sums involving harmonic numbers fall in the scope of classical hypergeometric algorithms. With this method, we give computer-assisted proofs for many known identities. Moreover, we establish several new combinatorial identities involving the generalized harmonic numbers.

Citation Download Citation

Huanhuan Zheng and Haitao Jin "The method of residue and identities on harmonic numbers", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 1216333 (22 April 2022); https://doi.org/10.1117/12.2627789

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