Probabilistic Degenerate Fubini Polynomials Associated with Random Variables

Author:

Xu Rongrong,Kim Taekyun,Kim Dae San,Ma Yuankui

Abstract

AbstractLet 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. As special cases of Y, we treat the gamma random variable with parameters $$\alpha ,\beta > 0$$ α , β > 0 , the Poisson random variable with parameter $$\alpha > 0$$ α > 0 , and the Bernoulli random variable with probability of success p.

Funder

The National Natural Science Foundation of China

Publisher

Springer Science and Business Media LLC

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