Some identities of extended degenerate r-central Bell polynomials arising from umbral calculus

Abstract

Extended degenerate r-central factorial numbers of the second kind and extended degenerate r-central Bell polynomials were introduced recently, as a degenerate version, a central analogue and an r-extension of Stirling numbers of the second kind and Bell polynomials, respectively, and various properties of them were investigated. The purpose of the present paper is to further derive some properties, recurrence relations and identities concerning those numbers and polynomials. In particular, we will represent the extended degenerate r-central Bell polynomials in terms of a good number of well-known special polynomials.