Degenerate central factorial numbers of the second kind

TL;DR

This paper introduces degenerate central factorial polynomials and numbers of the second kind, exploring their properties, identities, and recursive formulas, thus extending classical factorial concepts with a degeneracy parameter.

Contribution

It presents the first systematic study of degenerate central factorial polynomials and numbers of the second kind, including their properties and recursive relations.

Findings

Derived properties and identities for the degenerate polynomials and numbers

Established recursive formulas for these degenerate sequences

Extended classical factorial concepts with a degeneracy parameter

Abstract

In this paper, we introduce the degenerate central factorial polynomials and numbers of the second kind which are degenerate versions of the central factorial polynomials and numbers of the second kind. We derive some properties and identities for those polynomials and numbers. We obtain, among other things, recursive formulas for the degenerate central factorial polynomials and numbers of the second kind.