Higher-order degenerate harmonic numbers related to degenerate Riemann zeta function

TL;DR

This paper introduces and analyzes higher-order degenerate harmonic and hyperharmonic numbers, exploring their generating functions, explicit formulas, and relations, extending the degenerate harmonic number theory.

Contribution

It develops the theory of higher-order degenerate harmonic and hyperharmonic numbers, including their generating functions, explicit expressions, and relations, as well as their alternating versions.

Findings

Derived generating functions for higher-order degenerate harmonic numbers

Established explicit formulas for these numbers

Explored relations among different types of degenerate hyperharmonic numbers

Abstract

Recently, Kim-Kim investigated the degenerate harmonic numbers and the degenerate hyperharmonic numbers as degenerate versions of the harmonic numbers and the hyperharmonic numbers, respectively. The aim of this paper is to study the higher-order degenerate harmonic numbers and the higher-order degenerate hyperharmonic numbers as higher-order versions for the degenerate harmonic numbers and the degenerate hyperharmonic numbers, respectively. In addition, we study the higher-order alternating degenerate hyperharmonic numbers as an `alternating version' of the higher-order degenerate hyperharmonic numbers. In more detail, we find generating functions of them, explicit expressions for them and some relations among them for those three kinds of numbe