Degenerate central factorial numbers of the second kind

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. Recently, Dolgy and Kim (Proc Jangjeon Math Soc 21(2):309–317, 2018) obtained some explicit formulas of degenerate Stirling numbers associated with the degenerate special numbers and polynomials. This paper motivated our to do this research.