{
  "id": "2307.09277",
  "version": "v1",
  "published": "2023-07-18T14:15:24.000Z",
  "updated": "2023-07-18T14:15:24.000Z",
  "title": "Recurrence coefficients for orthogonal polynomials with a logarithmic weight function",
  "authors": [
    "Percy Deift",
    "Mateusz Piorkowski"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove an asymptotic formula for the recurrence coefficients of orthogonal polynomials with orthogonality measure $\\log \\big(\\frac{2}{1-x}\\big) dx$ on $(-1,1)$. The asymptotic formula confirms a special case of a conjecture by A. Magnus and extends earlier results by T. O. Conway and one of the authors. The proof relies on the Riemann-Hilbert method. The main difficulty in applying the method to the problem at hand is the lack of an appropriate local parametrix near the logarithmic singularity at $x = +1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-18T14:15:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "34M50",
      "45E05",
      "45M05"
    ],
    "keywords": [
      "logarithmic weight function",
      "orthogonal polynomials",
      "recurrence coefficients",
      "asymptotic formula confirms",
      "appropriate local parametrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}