{
  "id": "1906.03521",
  "version": "v1",
  "published": "2019-06-08T20:59:50.000Z",
  "updated": "2019-06-08T20:59:50.000Z",
  "title": "Asymptotic approximations of the continuous Hahn polynomials and their zeros",
  "authors": [
    "Li-Hua Cao",
    "Yu-Tian Li",
    "Yu Lin"
  ],
  "comment": "23 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Asymptotic approximations for the continuous Hahn polynomials and their zeros as the degree grows to infinity are established via their three-term recurrence relation. The methods are based on the uniform asymptotic expansions for difference equations developed by Wang and Wong (\\textit{Numer. Math.}, 2003) and the matching technique in the complex plane developed by Wang (\\textit{J. Approx. Theory}, 2014).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-08T20:59:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A60",
      "33C45"
    ],
    "keywords": [
      "continuous hahn polynomials",
      "asymptotic approximations",
      "three-term recurrence relation",
      "uniform asymptotic expansions",
      "complex plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}