About sum rules for Gould-Hopper polynomials

2011/03/26 by Olivier Lévêque, O. Lévêque, Lévêque, O. +3
Chemistry · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Advanced Statistical Methods and Models #FOS: Mathematics #Probability (math.PR) #Spectroscopy and Chemometric Analyses #math.PR

paper · pdf · doi:10.48550/arxiv.1103.5168

arxiv created 2011/03/26 · openalex publication_date 2011/03/26 · arxiv updated 2011/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that various identities from [1] and [3] involving Gould-Hopper polynomials can be deduced from the real but also complex orthogonal invariance of multivariate Gaussian distributions. We also deduce from this principle a useful stochastic representation for the inner product of two non-centered Gaussian vectors and two non-centered Gaussian matrices. [1] J. Daboul, S. S. Mizrahi, O(N) symmetries, sum rules for generalized Hermite polynomials and squeezed state, J. Phys. A: Math. Gen. 38 (2005) 427-448 [3] P. Graczyk, A. Nowak, A composition formula for squares of Hermite polynomials and its generalizations, C. R. Acad. Sci. Paris, Ser 1 338 (2004)

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