{
  "id": "0901.2639",
  "version": "v3",
  "published": "2009-01-17T14:31:59.000Z",
  "updated": "2010-11-16T09:08:38.000Z",
  "title": "A note on parameter derivatives of classical orthogonal polynomials",
  "authors": [
    "Radoslaw Szmytkowski"
  ],
  "comment": "8 pages, LaTeX; one reference added, some references updated",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Coefficients in the expansions of the form $\\partial P_{n}(\\lambda;z)}/\\partial\\lambda=\\sum_{k=0}^{n}a_{nk}(\\lambda)P_{k}(\\lambda;z)$, where $P_{n}(\\lambda;z)$ is the $n$th classical (the generalized Laguerre, Gegenbauer or Jacobi) orthogonal polynomial of variable $z$ and $\\lambda$ is a parameter, are evaluated. A method we adopt in the present paper differs from that used by Fr\\\"ohlich [Integral Transforms Spec. Funct. 2 (1994) 253] for the Jacobi polynomials and by Koepf [Integral Transforms Spec. Funct. 5 (1997) 69] for the generalized Laguerre and the Gegenbauer polynomials.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-11-16T09:08:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "33C45",
      "42C10"
    ],
    "keywords": [
      "classical orthogonal polynomials",
      "parameter derivatives",
      "integral transforms spec",
      "generalized laguerre",
      "jacobi polynomials"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0901.2639S"
    }
  }
}