{
  "id": "math/0301037",
  "version": "v1",
  "published": "2003-01-06T09:35:25.000Z",
  "updated": "2003-01-06T09:35:25.000Z",
  "title": "Orthogonality of Jacobi polynomials with general parameters",
  "authors": [
    "A. B. J. Kuijlaars",
    "A. Martinez-Finkelshtein",
    "R. Orive"
  ],
  "comment": "16 pages, 4 figures",
  "journal": "Electronic Transactions on Numerical Analysis 19 (2005), 1-17",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "In this paper we study the orthogonality conditions satisfied by Jacobi polynomials $P_n^{(\\alpha,\\beta)}$ when the parameters $\\alpha$ and $\\beta$ are not necessarily $>-1$. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a number of contours in the plane. In all cases we show that the orthogonality conditions characterize the Jacobi polynomial $P_n^{(\\alpha, \\beta)}$ of degree $n$ up to a constant factor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-01-06T09:35:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C45"
    ],
    "keywords": [
      "jacobi polynomial",
      "general parameters",
      "full orthogonality conditions",
      "multiple orthogonality conditions",
      "single contour"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......1037K"
    }
  }
}