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arXiv · 2601.19954

A General Multiplication Theorem for Multivariate Hermite Polynomials

Alistair Shilton
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Abstract

The multiplication theorem for univariate Hermite polynomials $H_k(\lambda x)$ is well-known. In this paper we generalize this result to multivariate Hermite polynomials ${\rm H}_{\bf k}({\mathbf{\Lambda}}{\bf x};{\mathbf{\Sigma}})$, and use this result to derive a multiplication theorem for univariate polynomials applied to inner-products $H_k({\mathbf{\lambda}}^{\rm T} {\bf x})$.

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Alistair Shilton. 2026-01-27. A General Multiplication Theorem for Multivariate Hermite Polynomials. https://arxiv.org/abs/2601.19954

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