{
  "id": "1601.08178",
  "version": "v1",
  "published": "2016-01-29T16:20:34.000Z",
  "updated": "2016-01-29T16:20:34.000Z",
  "title": "The orthogonality of Al-Salam-Carlitz polynomials for complex parameters",
  "authors": [
    "H. S. Cohl",
    "R. S. Costas-Santos",
    "W. Xu"
  ],
  "comment": "12 pages, 2 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this contribution, we study the orthogonality conditions satisfied by Al-Salam-Carlitz polynomials $U^{(a)}_n(x;q)$ when the parameters $a$ and $q$ are not necessarily real nor `classical', i.e., the linear functional $\\bf u$ with respect to such polynomial sequence is quasi-definite and not positive definite. We establish orthogonality on a simple contour in the complex plane which depends on the parameters. In all cases we show that the orthogonality conditions characterize the Al-Salam-Carlitz polynomials $U_n^{(a)}(x;q)$ of degree $n$ up to a constant factor. We also obtain a generalization of the unique generating function for these polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-29T16:20:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C45",
      "42C05"
    ],
    "keywords": [
      "al-salam-carlitz polynomials",
      "complex parameters",
      "orthogonality conditions",
      "polynomial sequence",
      "unique generating function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160108178C"
    }
  }
}