{
  "id": "1411.3045",
  "version": "v1",
  "published": "2014-11-12T01:56:57.000Z",
  "updated": "2014-11-12T01:56:57.000Z",
  "title": "Perturbations around the zeros of classical orthogonal polynomials",
  "authors": [
    "Ryu Sasaki"
  ],
  "comment": "LaTeX2e 31 pages, no figure",
  "categories": [
    "math.CA",
    "hep-th",
    "math-ph",
    "math.MP",
    "nlin.SI",
    "quant-ph"
  ],
  "abstract": "Starting from degree N solutions of a time dependent Schroedinger-like equation for classical orthogonal polynomials, a linear matrix equation describing perturbations around the N zeros of the polynomial is derived. The matrix has remarkable Diophantine properties. Its eigenvalues are independent of the zeros. The corresponding eigenvectors provide the representations of the lower degree (0,1,...,N-1) polynomials in terms of the zeros of the degree N polynomial. The results are valid universally for all the classical orthogonal polynomials, including the Askey scheme of hypergeometric orthogonal polynomials and its q-analogues.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-12T01:56:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classical orthogonal polynomials",
      "linear matrix equation describing perturbations",
      "hypergeometric orthogonal polynomials",
      "time dependent schroedinger-like equation",
      "diophantine properties"
    ],
    "publication": {
      "doi": "10.1063/1.4918707",
      "journal": "Journal of Mathematical Physics",
      "year": 2015,
      "month": "Apr",
      "volume": 56,
      "number": 4,
      "pages": "042106"
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1327510,
      "adsabs": "2015JMP....56d2106S"
    }
  }
}