The method of residue and identities on harmonic numbers
Huanhuan Zheng, Hai tao Jin · International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021) · 2022
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.