Integrals of products of Hermite functions
Wei-Min Wang
TL;DR
This paper calculates integrals of Hermite function products using generating functions and provides asymptotic estimates, which are relevant for analyzing solutions to certain nonlinear equations.
Contribution
It introduces a method to compute integrals of Hermite functions and derives their asymptotics, advancing understanding of their behavior in nonlinear contexts.
Findings
Explicit formulas for integrals of Hermite function products
Asymptotic estimates for four Hermite functions
Relevance to cubic nonlinear equations
Abstract
We compute the integrals of products of Hermite functions using the generating functions. The precise asymptotics of 4 Hermite functions are presented below. This estimate is relevant for the corresponding cubic nonlinear equation.
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Taxonomy
TopicsPolynomial and algebraic computation · Mathematical functions and polynomials · Nonlinear Waves and Solitons