Several expressions for degenerate harmonic numbers and some related numbers

TL;DR

This paper derives explicit formulas for degenerate harmonic numbers and explores related numbers, providing new insights into their structure and connections to classical harmonic numbers.

Contribution

It introduces several explicit expressions for degenerate harmonic numbers and examines related numbers, extending the understanding of their properties and relationships.

Findings

Derived explicit formulas for degenerate harmonic numbers

Analyzed degenerate harmonic numbers of order m and related numbers

Connected related numbers to classical harmonic numbers when m=1

Abstract

Many authors have recently studied the degenerate harmonic numbers. This paper makes two main contributions. First, we derive several explicit expressions for these numbers, which are a degenerate version of the ordinary harmonic numbers. We also examine the degenerate harmonic numbers of order m and find an expression for them. Second, we investigate some related numbers that are closely connected to the degenerate harmonic numbers of order m, which reduce to the degenerate harmonic numbers when m=1