About sum rules for Gould-Hopper polynomials
Probability
2011-03-29 v1
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)
Cite
@article{arxiv.1103.5168,
title = {About sum rules for Gould-Hopper polynomials},
author = {O. Lévêque and C. Vignat},
journal= {arXiv preprint arXiv:1103.5168},
year = {2011}
}