{
  "id": "1103.5168",
  "version": "v1",
  "published": "2011-03-26T21:51:46.000Z",
  "updated": "2011-03-26T21:51:46.000Z",
  "title": "About sum rules for Gould-Hopper polynomials",
  "authors": [
    "O. Lévêque",
    "C. Vignat"
  ],
  "categories": [
    "math.PR"
  ],
  "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)",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-26T21:51:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gould-hopper polynomials",
      "sum rules",
      "multivariate gaussian distributions",
      "complex orthogonal invariance",
      "inner product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.5168L"
    }
  }
}