{
  "id": "2111.11663",
  "version": "v2",
  "published": "2021-11-23T06:00:39.000Z",
  "updated": "2022-06-28T02:18:05.000Z",
  "title": "Asymptotic behaviours of q-orthogonal polynomials from a q-Riemann Hilbert Problem",
  "authors": [
    "Nalini Joshi",
    "Tomas Lasic Latimer"
  ],
  "comment": "23 pages, 1 figure",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We describe a Riemann-Hilbert problem for a family of $q$-orthogonal polynomials, $\\{ P_n(x) \\}_{n=0}^\\infty$, and use it to deduce their asymptotic behaviours in the limit as the degree, $n$, approaches infinity. We find that the $q$-orthogonal polynomials studied in this paper share certain universal behaviours in the limit $n\\to\\infty$. In particular, we observe that the asymptotic behaviour near the location of their smallest zeros, $x \\sim q^{n/2}$, and norm, $\\|P_n\\|_2$, are independent of the weight function as $n\\to\\infty$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-06-28T02:18:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic behaviour",
      "q-riemann hilbert problem",
      "q-orthogonal polynomials",
      "approaches infinity",
      "smallest zeros"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}