Summation formulas of hyperharmonic numbers with their generalizations II

2021/03/19 by Komatsu, Takao, Li, Rusen
#05A19 #11B65 #11B73 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2103.10658

Abstract

In 1990, Spieß gave some identities of harmonic numbers including the types of ∑_ℓ=1ⁿℓ^k H_ℓ, ∑_ℓ=1ⁿℓ^k H_n-ℓ and ∑_ℓ=1ⁿℓ^k H_ℓ H_n-ℓ. In this paper, we derive several formulas of hyperharmonic numbers including ∑_ℓ=0ⁿ ℓ^p h_ℓ^(r) h_n-ℓ^(s) and ∑_ℓ=0ⁿ ℓ^p(h_ℓ^(r))². Some more formulas of generalized hyperharmonic numbers are also shown.

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