Some results on degenerate harmonic numbers and degenerate Fubini polynomials

TL;DR

This paper explores properties of degenerate harmonic and Fubini polynomials using a general identity involving degenerate r-Stirling numbers, contributing to the understanding of degenerate special numbers and polynomials.

Contribution

It introduces new results on degenerate harmonic, hyperharmonic, and Fubini polynomials based on a general identity involving degenerate r-Stirling numbers.

Findings

Derived identities for degenerate harmonic numbers

Established relations for degenerate Fubini polynomials

Connected degenerate numbers with formal power series

Abstract

In recent years, some degenerate versions of quite a few special numbers and polynomials are introduced and investigated by means of various methods. The aim of this paper is to study some results on degenerate harmonic numbers, degenerate hyperharmonic numbers, degenerate Fubi polynomials and degenerate r-Fubini polynomials from a general identity which is valid for any two formal power series and involves the degenerate r-Stirling numbers of the second kind.