Euler sums of generalized hyperharmonic numbers

Abstract

In this paper, we mainly show that Euler sums of generalized hyperharmonic numbers can be expressed in terms of linear combinations of the classical Euler sums.

Euler sums of generalized alternating hyperharmonic numbers II

“…Since hyperharmonic and generalized (alternating) hyperharmonic numbers are hyper-generalizations of harmonic numbers, their Euler sums (see [6,7,9,11,12,15,16] for example) may have interesting relations with the Riemann zeta function.…”

“…For r = 1, 2, 3, ζ H (p,r) (m) were also written explicitly by means of (multiple) zeta values. By computing a series of special polynomials, the author [11] obtain a nice formula for the generalized hyperharmonic numbers H (p,r) n . As a corollary, the author proved that ζ H (p,r) (m) could be expressed as linear combinations of classical Euler sums.…”