Combinatorial identities related to degenerate Stirling numbers of the second kind

TL;DR

This paper explores properties, identities, and recurrence relations of degenerate Stirling numbers of the second kind, which are important in the study of degenerate special polynomials and numbers.

Contribution

It provides new properties, identities, and explicit formulas for degenerate Stirling numbers of the second kind, enhancing understanding of their role in degenerate polynomial theory.

Findings

Derived new recurrence relations for degenerate Stirling numbers

Established explicit expressions for these numbers

Connected degenerate Stirling numbers with degenerate Euler polynomials

Abstract

The study of degenerate versions of certain special polynomials and numbers, which was initiated by Carlitz's work on degenerate Euler and degenerate Bernoulli polynomials, has recently seen renewed interest among mathematicians. The aim of this paper is to study some properties, certain identities, recurrence relations and explicit expressions for degenerate Stirling numbers of the second kind, which are a degenerate version of the Stirling numbers of the second kind. These numbers appear very frequently when we study various degenerate versions of many special polynomials and numbers. Especially, we consider some closely related polynomials and power series in connection with a degenerate version of Euler's formula for the Stirling numbers of the second kind.