A note on the generalized Bernoulli and Euler Polynomials

TL;DR

This paper employs probabilistic techniques to derive new properties of generalized Bernoulli and Euler polynomials using Appell polynomial frameworks linked to specific random variables.

Contribution

It introduces a novel probabilistic approach to analyze generalized Bernoulli and Euler polynomials through Appell polynomial properties associated with specific distributions.

Findings

Derived new identities for generalized Bernoulli and Euler polynomials

Connected polynomial properties with probabilistic distributions

Enhanced understanding of polynomial structures via probabilistic methods

Abstract

In this paper we use probabilistic methods to derive some results on the generalized Bernoulli and generalized Euler polynomials. Our approach is based on the properties of Appell polynomials associated with uniformly distributed and Bernoulli distributed random variables and their sums.