{
  "id": "math/0703546",
  "version": "v1",
  "published": "2007-03-19T10:47:16.000Z",
  "updated": "2007-03-19T10:47:16.000Z",
  "title": "Quantum Hilbert matrices and orthogonal polynomials",
  "authors": [
    "Jorgen Ellegaard Andersen",
    "Christian Berg"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Using the notion of quantum integers associated with a complex number $q\\neq 0$, we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little $q$-Jacobi polynomials when $|q|<1$, and for the special value $q=(1-\\sqrt{5})/(1+\\sqrt{5})$ they are closely related to Hankel matrices of reciprocal Fibonacci numbers called Filbert matrices. We find a formula for the entries of the inverse quantum Hilbert matrix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-19T10:47:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D45",
      "11B39"
    ],
    "keywords": [
      "quantum hilbert matrices",
      "orthogonal polynomials",
      "hankel matrices",
      "inverse quantum hilbert matrix",
      "reciprocal fibonacci numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3546E"
    }
  }
}