{
  "id": "1202.5165",
  "version": "v1",
  "published": "2012-02-23T12:56:51.000Z",
  "updated": "2012-02-23T12:56:51.000Z",
  "title": "A probabilistic proof of product formulas for spherical Bessel functions and their matrix analogues",
  "authors": [
    "Luc Deleaval",
    "Nizar Demni"
  ],
  "categories": [
    "math.PR",
    "math.GR"
  ],
  "abstract": "We write, for geometric index values, a probabilistic proof of the product formula for spherical Bessel functions. Our proof has the merit to carry over without any further effort to Bessel-type hypergeometric functions of one matrix argument. Moreover, the representative probability distribution involved in the matrix setting is shown to be closely related to matrix-variate normal distributions and to the symmetrization of upper-left corners of Haar distributed orthogonal matrices. Once we did, we use the latter relation to perform a detailed analysis of this probability distribution. In case it is absolutely continuous with respect to Lebesgue measure on the space of real symmetric matrices, the product formula for Bessel-type hypergeometric functions of two matrix arguments is obtained from Weyl integration formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-23T12:56:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spherical bessel functions",
      "product formula",
      "probabilistic proof",
      "matrix analogues",
      "bessel-type hypergeometric functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.5165D"
    }
  }
}