Probabilistic Representation of Bernoulli, Euler and Carlitz Hermite Polynomials

TL;DR

This paper explores Bernoulli, Euler, and Carlitz Hermite polynomials using a probabilistic approach to provide new insights into their properties and relationships.

Contribution

It introduces a probabilistic framework to analyze classical polynomials, extending the umbral approach of Gessel with novel probabilistic interpretations.

Findings

Probabilistic representations of Bernoulli, Euler, and Carlitz Hermite polynomials.

New relationships between these polynomials uncovered through probabilistic methods.

Enhanced understanding of polynomial properties via probabilistic analysis.

Abstract

We revisit in a probabilistic framework the umbral approach of Bernoulli, Euler and Carlitz Hermite polynomials by Gessel [1].