{
  "id": "1805.11855",
  "version": "v1",
  "published": "2018-05-30T08:40:54.000Z",
  "updated": "2018-05-30T08:40:54.000Z",
  "title": "Rational extension of Newton diagram for the positivity of ${}_1F_2$ hypergeometric functions and Askey-Szegö problem",
  "authors": [
    "Yong-Kum Cho",
    "Seok-Young Chung",
    "Hera Yun"
  ],
  "comment": "23 pages, 6 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "We present a rational extension of Newton diagram for the positivity of ${}_1F_2$ generalized hypergeometric functions. As an application, we give upper and lower bounds for the transcendental roots $\\beta(\\alpha)$ of \\begin{align*} \\int_0^{j_{\\alpha, 2}} t^{-\\beta} J_\\alpha(t) dt = 0\\qquad(-1<\\alpha\\le 1/2), \\end{align*} where $j_{\\alpha, 2}$ denotes the second positive zero of Bessel function $J_\\alpha$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-30T08:40:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D15",
      "33C10",
      "33C20"
    ],
    "keywords": [
      "newton diagram",
      "rational extension",
      "positivity",
      "lower bounds",
      "transcendental roots"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}