Hermite Calculus

TL;DR

This paper introduces a novel umbral-based calculus for Hermite and Hermite-like polynomials, enabling algebraic manipulation and simplifying computational tasks involving these polynomials.

Contribution

It presents a new algebraic method that treats blocks of Hermite polynomials as independent quantities, facilitating easier calculations.

Findings

Simplifies computations involving Hermite polynomials

Provides practical rules for algebraic manipulation

Enhances the theoretical framework for Hermite calculus

Abstract

We develop a new method of umbral nature to treat blocks of Hermite and of Hermite like polynomials as independent algebraic quantities. The Calculus we propose allows the formulation of a number of practical rules allowing significant simplifications in computational problems.