Euler sums of generalized alternating hyperharmonic numbers II

TL;DR

This paper introduces a new class of generalized alternating hyperharmonic numbers and demonstrates that their Euler sums can be expressed as linear combinations of classical Euler sums, expanding the understanding of hyperharmonic number properties.

Contribution

The paper defines a new type of generalized alternating hyperharmonic numbers and relates their Euler sums to classical Euler sums, providing a novel analytical framework.

Findings

Euler sums of the new hyperharmonic numbers are expressible via classical Euler sums.

The paper establishes a linear combination representation for these sums.

It extends the analytical tools available for hyperharmonic number analysis.

Abstract

In this paper, we introduce a new type of generalized alternating hyperharmonic numbers $H_n^{(p,r,s_{1},s_{2})}$, and show that Euler sums of the generalized alternating hyperharmonic numbers $H_n^{(p,r,s_{1},s_{2})}$ can be expressed in terms of linear combinations of classical (alternating) Euler sums.