{
  "id": "1210.5305",
  "version": "v1",
  "published": "2012-10-19T03:37:59.000Z",
  "updated": "2012-10-19T03:37:59.000Z",
  "title": "A generalization of the Mehta-Wang determinant and Askey-Wilson polynomials",
  "authors": [
    "Masao Ishikawa",
    "Hiroyuki Tagawa",
    "Jiang Zeng"
  ],
  "comment": "25 pages",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Motivated by the Gaussian symplectic ensemble, Mehta and Wang evaluated the $n$ by $n$ determinant $\\det((a+j-i)\\Gamma(b+j+i))$ in 2000. When $a=0$, Ciucu and Krattenthaler computed the associated Pfaffian $\\Pf((j-i)\\Gamma(b+j+i))$ with an application to the two dimensional dimer system in 2011. Recently we have generalized the latter Pfaffian formula with a $q$-analogue by replacing the Gamma function by the moment sequence of the little $q$-Jacobi polynomials. On the other hand, Nishizawa has found a $q$-analogue of the Mehta--Wang formula. Our purpose is to generalize both the Mehta-Wang and Nishizawa formulae by using the moment sequence of the little $q$-Jacobi polynomials. It turns out that the corresponding determinant can be evaluated explicitly in terms of the Askey-Wilson polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-19T03:37:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A30"
    ],
    "keywords": [
      "askey-wilson polynomials",
      "mehta-wang determinant",
      "jacobi polynomials",
      "moment sequence",
      "generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.5305I"
    }
  }
}