Evaluation of Euler-like sums via Hurwitz zeta values

Abstract

In this paper we collect two generalizations of harmonic numbers (namely generalized harmonic numbers and hyperharmonic numbers) under one roof. Recursion relations, closed-form evaluations, and generating functions of this unified extension are obtained. In light of this notion we evaluate some particular values of Euler sums in terms of odd zeta values. We also consider the noninteger property and some arithmetical aspects of this unified extension.

Applications of derivative and difference operators on some sequences

“…n := 1/n, (n ≥ 1) and h (r) 0 := 0, (r ≥ 0). Hyperharmonic numbers are closely related to analytic number theory (see [2,5,11,13,19]), discrete mathematics and combinatorial analysis (see [3,8,10,12]).…”

Sums Over Primes II

“…n := n j=1 1/j p and taking repeated partial sums, Dil, Mező and Cenkci [3] introduced the generalized hyperharmonic numbers…”

Generalized Hyperharmonic Number Sums With Reciprocal Binomial Coefficients

“…Let Z, N, N 0 and C denote the set of integers, positive integers, nonnegative integers and complex numbers, respectively. In the present paper, we mainly study the so-called generalized hyperharmonic numbers [11,15,19] which are defined as…”