{
  "id": "1307.3906",
  "version": "v1",
  "published": "2013-07-15T12:17:21.000Z",
  "updated": "2013-07-15T12:17:21.000Z",
  "title": "On a formula of T. Rivoal",
  "authors": [
    "Jean-Paul Allouche"
  ],
  "journal": "Annales Univ. Sci. Budapest., Sect. Comp. 40 (2013) 69--79",
  "categories": [
    "math.NT"
  ],
  "abstract": "In an unpublished 2005 paper T. Rivoal proved a formula giving 4/pi as the infinite product of factors (1 + 1/(k+1)) to a power involving the integer part of the logarithm of k in base 2 and a 4-periodic sequence. We show how a lemma in a 1988 paper of J. Shallit and the author allows us to prove that formula, as well as a family of similar formulas involving occurrences of blocks of digits in the base-B expansion of the integer k, where B is an integer larger than 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-15T12:17:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Y60",
      "11A63",
      "11A67"
    ],
    "keywords": [
      "infinite product",
      "integer part",
      "similar formulas",
      "base-b expansion",
      "integer larger"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.3906A"
    }
  }
}