{
  "id": "2403.18669",
  "version": "v1",
  "published": "2024-03-27T15:13:26.000Z",
  "updated": "2024-03-27T15:13:26.000Z",
  "title": "Orthogonal Polynomials with a Singularly Perturbed Airy Weight",
  "authors": [
    "Chao Min",
    "Yuan Cheng"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the monic orthogonal polynomials with respect to a singularly perturbed Airy weight. By using Chen and Ismail's ladder operator approach, we derive a discrete system satisfied by the recurrence coefficients for the orthogonal polynomials. We find that the orthogonal polynomials satisfy a second-order linear ordinary differential equation, whose coefficients are all expressed in terms of the recurrence coefficients. By considering the time evolution, we obtain a system of differential-difference equations satisfied by the recurrence coefficients. Finally, we study the asymptotics of the recurrence coefficients when the degrees of the orthogonal polynomials tend to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-27T15:13:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C45",
      "42C05"
    ],
    "keywords": [
      "singularly perturbed airy weight",
      "recurrence coefficients",
      "second-order linear ordinary differential equation",
      "ismails ladder operator approach",
      "monic orthogonal polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}