{
  "id": "1403.1374",
  "version": "v2",
  "published": "2014-03-06T08:29:18.000Z",
  "updated": "2014-07-16T14:15:37.000Z",
  "title": "Orthogonal polynomials for Minkowski's question mark function",
  "authors": [
    "Zoé Dresse",
    "Walter Van Assche"
  ],
  "comment": "26 pages, 11 figures, 4 tables",
  "categories": [
    "math.CA"
  ],
  "abstract": "Hermann Minkowski introduced a function in 1904 which maps quadratic irrational numbers to rational numbers and this function is now known as Minkowski's question mark function since Minkowski used the notation $?(x)$. This function is a distribution function on $[0,1]$ which defines a singular continuous measure with support $[0,1]$. Our interest is in the (monic) orthogonal polynomials $(P_n)_{n \\in \\mathbb{N}}$ for the Minkowski measure and in particular in the behavior of the recurrence coefficients of the three term recurrence relation. We will give some numerical experiments using the discretized Stieltjes-Gautschi method with a discrete measure supported on the Minkowski sequence. We also explain how one can compute the moments of the Minkowski measure and compute the recurrence coefficients using the Chebyshev algorithm.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-16T14:15:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "11A45",
      "11B57",
      "65Q30"
    ],
    "keywords": [
      "minkowskis question mark function",
      "orthogonal polynomials",
      "maps quadratic irrational numbers",
      "recurrence coefficients",
      "minkowski measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.1374D"
    }
  }
}