{
  "id": "2209.07128",
  "version": "v1",
  "published": "2022-09-15T08:22:56.000Z",
  "updated": "2022-09-15T08:22:56.000Z",
  "title": "Differential and Difference Equations for Recurrence Coefficients of Orthogonal Polynomials with a Singularly Perturbed Laguerre-type Weight",
  "authors": [
    "Chao Min",
    "Yuan Cheng",
    "Yang Chen"
  ],
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We are concerned with the monic orthogonal polynomials with respect to a singularly perturbed Laguerre-type weight. By using the ladder operator approach, we derive a complicated system of nonlinear second-order difference equations satisfied by the recurrence coefficients. This allows us to derive the large $n$ asymptotic expansions of the recurrence coefficients. In addition, we also obtain a system of differential-difference equations for the recurrence coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-15T08:22:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "41A60"
    ],
    "keywords": [
      "singularly perturbed laguerre-type weight",
      "recurrence coefficients",
      "nonlinear second-order difference equations",
      "ladder operator approach",
      "monic orthogonal polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}