A General Multiplication Theorem for Multivariate Hermite Polynomials
Abstract
The multiplication theorem for univariate Hermite polynomials $H_k(λx)$ is well-known. In this paper we generalize this result to multivariate Hermite polynomials ${\rm H}_{\bf k}({\mathbfΛ}{\bf x};{\mathbfΣ})$, and use this result to derive a multiplication theorem for univariate polynomials applied to inner-products $H_k({\mathbfλ}^{\rm T} {\bf x})$.
Fields of Study & Subjects
Mathematical functions and polynomials
Advanced Combinatorial Mathematics
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 27 January 2026
- Document type
- Preprint