A General Multiplication Theorem for Multivariate Hermite Polynomials
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908793091129344 |
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| author | Shilton, Alistair |
| author_facet | Shilton, Alistair |
| contents | 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 $H_k({\mathbfλ}^{\rm T} {\bf x})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19954 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A General Multiplication Theorem for Multivariate Hermite Polynomials Shilton, Alistair General Mathematics 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 $H_k({\mathbfλ}^{\rm T} {\bf x})$. |
| title | A General Multiplication Theorem for Multivariate Hermite Polynomials |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2601.19954 |