A Probabilistic Extension of the Fubini Polynomials

2023/12/23 by Raminder Singh Soni, Ashok Kumar Pathak, Soni, R. +3 · 1 citation
Mathematics · #05A19 #11C08 #FOS: Mathematics #Mathematical functions and polynomials #Primary : 60E05 #Probability (math.PR) #Secondary : 11B73

paper · pdf · doi:10.48550/arxiv.2312.15193

openalex publication_date 2023/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Degenerate Sheffer-type polynomials and degenerate Sheffer polynomials associated with a random variable

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• Probabilistic degenerate Fubini polynomials associated with random variables
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