{
  "id": "1206.4737",
  "version": "v1",
  "published": "2012-06-20T23:15:46.000Z",
  "updated": "2012-06-20T23:15:46.000Z",
  "title": "Plancherel_Rotach Asymptotics for q-Orthogonal Polynomials",
  "authors": [
    "Mourad E. H. Ismail",
    "Xin Li"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We establish the Plancherel-Rotach-type asymptotics around the largest zero (the soft edge asymptotics) for some classes of polynomials satisfying three-term recurrence relations with exponentially increasing coefficients. As special cases, our results include this type of asymptotics for q^{-1}-Hermite polynomials of Askey, Ismail and Masson, q-Laguerre polynomials, and the Stieltjes-Wigert polynomials. We also introduce a one parameter family of solutions to the q-difference equation of the Ramanujan function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-20T23:15:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D45",
      "41A60",
      "65Q30"
    ],
    "keywords": [
      "q-orthogonal polynomials",
      "polynomials satisfying three-term recurrence relations",
      "soft edge asymptotics",
      "largest zero",
      "plancherel-rotach-type asymptotics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.4737I"
    }
  }
}