Some results on a class of generalized harmonic numbers

Abstract

In this paper, we investigate properties of a class of generalized harmonic numbers H _n,k,r(α, β). By means of the method of coefficient, we derive a series of identities for H _n,k,r,(α, β). We give the asymptotic expansion of H _n,k,r,(α,β) when k and r are fixed. Further more we discuss the computation of sums for H _n,k,r(α,β) and inverse of binomial coefficient. We give integral representations for sums involving H _n,k,r(α,β) and inverse of binomial coefficient.