On integrals involving Hermite polynomials

TL;DR

This paper introduces a method combining generating functions and multivariable Hermite polynomial theory to evaluate complex integrals involving Gaussian functions and Hermite polynomial products.

Contribution

It presents a novel approach that simplifies the calculation of integrals with Hermite polynomials using combined generating function and multivariable polynomial techniques.

Findings

Effective evaluation of Gaussian and Hermite polynomial integrals

Simplification of complex integral calculations

Potential applications in mathematical physics and probability

Abstract

We show how the combined use of the generating function method and of the theory of multivariable Hermite polynomials is naturally suited to evaluate integrals of gaussian functions and of multiple products of Hermite polynomials.