{
  "id": "1708.07729",
  "version": "v1",
  "published": "2017-08-25T13:30:45.000Z",
  "updated": "2017-08-25T13:30:45.000Z",
  "title": "Hankel determinant of the Rayleigh sums of zeros of Bessel functions",
  "authors": [
    "Árpád Baricz"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this note a new proof for the classical theorem of Hurwitz on the exact number of complex zeros of Bessel functions of the first kind is given. The proof is based on the closed form of the determinant of a symmetric Hankel matrix whose terms are Rayleigh sums of the zeros of Bessel functions and on some new interesting results on entire functions of finite growth order of Kytmanov and Khodos [khodos].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-25T13:30:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30D15",
      "30D10",
      "33C10"
    ],
    "keywords": [
      "bessel functions",
      "rayleigh sums",
      "hankel determinant",
      "finite growth order",
      "symmetric hankel matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}