{
  "id": "1002.2666",
  "version": "v2",
  "published": "2010-02-13T01:10:47.000Z",
  "updated": "2010-03-04T18:24:08.000Z",
  "title": "Exceptional orthogonal polynomials and the Darboux transformation",
  "authors": [
    "David Gomez-Ullate",
    "Niky Kamran",
    "Robert Milson"
  ],
  "comment": "corrected abstract, added references, minor corrections",
  "journal": "J. Phys. A 43 (2010) 434016",
  "doi": "10.1088/1751-8113/43/43/434016",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We adapt the notion of the Darboux transformation to the context of polynomial Sturm-Liouville problems. As an application, we characterize the recently described $X_m$ Laguerre polynomials in terms of an isospectral Darboux transformation. We also show that the shape-invariance of these new polynomial families is a direct consequence of the permutability property of the Darboux-Crum transformation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-03-04T18:24:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C45",
      "33C47"
    ],
    "keywords": [
      "exceptional orthogonal polynomials",
      "polynomial sturm-liouville problems",
      "isospectral darboux transformation",
      "darboux-crum transformation",
      "permutability property"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2010,
      "month": "Oct",
      "volume": 43,
      "pages": 434016
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JPhA...43Q4016G"
    }
  }
}