Some results on degenerate Fubini and degenerate Bell polynomials

TL;DR

This paper explores properties and identities of degenerate Fubini and Bell polynomials, providing new expressions for their generating functions and extending understanding of their combinatorial and algebraic structures.

Contribution

It introduces new identities and expressions for the generating functions of degenerate Fubini and Bell polynomials, advancing their theoretical understanding.

Findings

Derived new formulas for generating functions

Established identities relating to degenerate polynomials

Extended combinatorial interpretations of degenerate polynomials

Abstract

The aim of this paper is to further study some properties and identities on the degenerate Fubini and the degenerate Bell polynomials which are degenerate versions of the Fubini and the Bell polynomials, respectively. Especially, we find several expressions for the generating function of the sum of the values of the generalized falling factorials at positive consecutive integers.