Bernoulli type polynomials on Umbral Algebra

TL;DR

This paper explores generating functions for modified Milne-Thomson's polynomials related to Bernoulli and Hermite polynomials using Umbral algebra, deriving new identities for these polynomials.

Contribution

It introduces a novel application of Umbral algebra to generate identities for modified Milne-Thomson's polynomials connected to Bernoulli and Hermite polynomials.

Findings

Derived new identities for Bernoulli and Hermite related polynomials.

Established connections between generating functions and Umbral algebra.

Enhanced understanding of polynomial modifications through algebraic methods.

Abstract

The aim of this paper is to investigate generating functions for modification of the Milne-Thomson's polynomials, which are related to the Bernoulli polynomials and the Hermite polynomials. By applying the Umbral algebra to these generating functions, we provide to deriving identities for these polynomials.