{
  "id": "1612.00927",
  "version": "v1",
  "published": "2016-12-03T05:34:00.000Z",
  "updated": "2016-12-03T05:34:00.000Z",
  "title": "Simplified Expressions of the Multi-indexed Laguerre and Jacobi Polynomials",
  "authors": [
    "Satoru Odake",
    "Ryu Sasaki"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CA",
    "hep-th",
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "The multi-indexed Laguerre and Jacobi polynomials form a complete set of orthogonal polynomials. They satisfy second order differential equations but not three term recurrence relations, because of the `holes' in their degrees. The multi-indexed Laguerre and Jacobi polynomials have Wronskian expressions originating from multiple Darboux transformations. For the ease of applications, two different forms of simplified expressions of the multi-indexed Laguerre and Jacobi polynomials are derived based on various identities. The parity transformation property of the multi-indexed Jacobi polynomials is derived based on that of the Jacobi polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-03T05:34:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multi-indexed laguerre",
      "simplified expressions",
      "satisfy second order differential equations",
      "jacobi polynomials form",
      "term recurrence relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}