Abstract
Let \(Y\) be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to study probabilistic Bernoulli polynomials of order \(r\) associated with \(Y\) and probabilistic multi-poly-Bernoulli polynomials associated with \(Y\) . They are respectively probabilistic extensions of Bernoulli polynomials of order \(r\) and multi-poly-Bernoulli polynomials. We find explicit expressions, certain related identities and some properties for them. In addition, we treat the special cases of Poisson, gamma and Bernoulli random variables.
DOI 10.1134/S1061920824030087
