Probabilistic degenerate Fubini polynomials associated with random variables

TL;DR

This paper introduces probabilistic versions of degenerate Fubini polynomials linked to a random variable with an existing moment generating function, exploring their properties, identities, and recurrence relations.

Contribution

It develops the theory of probabilistic degenerate Fubini polynomials associated with a random variable, including explicit formulas and key identities.

Findings

Derived explicit expressions for the polynomials

Established recurrence relations and identities

Explored properties related to the associated random variable

Abstract

Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and the degenerate Fubini polynomials of order $r$, namely the probabilisitc degenerate Fubini polynomials associated with Y and the probabilistic degenerate Fubini polynomials of order r associated with Y. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials.