{
  "id": "1107.2236",
  "version": "v1",
  "published": "2011-07-12T10:21:40.000Z",
  "updated": "2011-07-12T10:21:40.000Z",
  "title": "Asymptotic zero distribution of a class of hypergeometric polynomials",
  "authors": [
    "K. A. Driver",
    "S. J. Johnston"
  ],
  "journal": "Quaestiones Mathematicae 30(2007), 219-230",
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove that the zeros of ${}_2F_1(-n,\\frac{n+1}{2};\\frac{n+3}{2};z)$ asymptotically approach the section of the lemniscate $\\{z: |z(1-z)^2|=4/27; \\textrm{Re}(z)>1/3\\}$ as $n\\rightarrow \\infty$. In recent papers (cf. \\cite{KMF}, \\cite{orive}), Mart\\'inez-Finkelshtein and Kuijlaars and their co-authors have used Riemann-Hilbert methods to derive the asymptotic zero distribution of Jacobi polynomials $P_n^{(\\alpha_n,\\beta_n)}$ when the limits $\\ds A=\\lim_{n\\rightarrow \\infty}\\frac{\\alpha_n}{n}$ and $\\ds B=\\lim_{n\\rightarrow \\infty}\\frac{\\beta_n}{n}$ exist and lie in the interior of certain specified regions in the $AB$-plane. Our result corresponds to one of the transitional or boundary cases for Jacobi polynomials in the Kuijlaars Mart\\'inez-Finkelshtein classification.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-12T10:21:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C05",
      "30C15"
    ],
    "keywords": [
      "asymptotic zero distribution",
      "hypergeometric polynomials",
      "jacobi polynomials",
      "kuijlaars martinez-finkelshtein classification",
      "result corresponds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.2236D"
    }
  }
}