A Probabilistic Extension of the Fubini Polynomials
Probability
2023-12-27 v1
Abstract
In this paper, we present a probabilistic extension of the Fubini polynomials and numbers associated with a random variable satisfying some appropriate moment conditions. We obtain the exponential generating function and an integral representation for it. The higher order Fubini polynomials and recurrence relations are also derived. A probabilistic generalization of a series transformation formula and some interesting examples are discussed. A connection between the probabilistic Fubini polynomials and Bernoulli, Poisson, and geometric random variables are also established. Finally, a determinant expression formula is presented.
Keywords
Cite
@article{arxiv.2312.15193,
title = {A Probabilistic Extension of the Fubini Polynomials},
author = {R. Soni and A. K. Pathak and P. Vellaisamy},
journal= {arXiv preprint arXiv:2312.15193},
year = {2023}
}