{
  "id": "1411.7299",
  "version": "v1",
  "published": "2014-11-26T17:04:30.000Z",
  "updated": "2014-11-26T17:04:30.000Z",
  "title": "Two-variable $-1$ Jacobi polynomials",
  "authors": [
    "Vincent X. Genest",
    "Jean-Michel Lemay",
    "Luc Vinet",
    "Alexei Zhedanov"
  ],
  "comment": "13 pp",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "A two-variable generalization of the Big $-1$ Jacobi polynomials is introduced and characterized. These bivariate polynomials are constructed as a coupled product of two univariate Big $-1$ Jacobi polynomials. Their orthogonality measure is obtained. Their bispectral properties (eigenvalue equations and recurrence relations) are determined through a limiting process from the two-variable Big $q$-Jacobi polynomials of Lewanowicz and Wo\\'zny. An alternative derivation of the weight function using Pearson-type equations is presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-26T17:04:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C50"
    ],
    "keywords": [
      "jacobi polynomials",
      "two-variable",
      "recurrence relations",
      "pearson-type equations",
      "bivariate polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.7299G"
    }
  }
}