Poisson degenerate central moments related to degenerate Dowling and degenerate r-Dowling polynomials

TL;DR

This paper explores the connections between degenerate Dowling polynomials, Poisson degenerate central moments, and Charlier polynomials, revealing new relationships in the context of degenerate polynomial families.

Contribution

It establishes novel links between degenerate Dowling polynomials, Poisson degenerate central moments, and Charlier polynomials, expanding the theoretical understanding of these polynomial families.

Findings

Derived formulas connecting degenerate Dowling polynomials with Poisson degenerate central moments.

Demonstrated relationships between degenerate Dowling polynomials and Charlier polynomials.

Provided new insights into the structure of degenerate polynomial families.

Abstract

Degenerate Dowling and degenerate r-Dowling polynomials were introduced earlier as degenerate versions and further generalizations of Dowling and r-Dowling polynomials. The aim of this paper is to show their connections with Poisson degenerate central moments for a Poisson random variable with a certain parameter and with Charlier polynomials.