SOME IDENTITIES OF FULLY DEGENERATE DOWLING AND FULLY DEGENERATE BELL POLYNOMIALS ARISING FROM λ-UMBRAL CALCULUS

Abstract

Recently, Kim–Kim introduced the [Formula: see text]-umbral calculus, in which the [Formula: see text]-Sheffer sequences occupy the central position. In this paper, we introduce the fully degenerate Bell and the fully degenerate Dowling polynomials, and investigate some properties and identities relating to those polynomials with the help of [Formula: see text]-umbral calculus. Here, we note that the fully degenerate Bell poynomials and the fully degenerate Dowling polynomials are, respectively, degenerate versions of the Bell polynomials and the Dowling polynomials, of which the latters are the natural extension of the Whitney numbers of the second kind.