{
  "id": "2009.02025",
  "version": "v1",
  "published": "2020-09-04T06:57:46.000Z",
  "updated": "2020-09-04T06:57:46.000Z",
  "title": "Transcendental Infinite Products Associated with the $\\pm 1$ Thue-Morse Sequence",
  "authors": [
    "László Tóth"
  ],
  "journal": "Journal of Integer Sequences, Vol. 23 (2020), Article 20.8.2",
  "categories": [
    "math.NT"
  ],
  "abstract": "Infinite products associated with the $\\pm 1$ Thue-Morse sequence whose value is rational or algebraic irrational have been studied by several authors. In this short note we prove three new infinite product identities involving ${\\pi}$, $\\sqrt{2}$, and the $\\pm 1$ Thue-Morse sequence, building on a result by Allouche, Riasat, and Shallit. We then use our method to find a new expression for a product appearing within the context of the Flajolet-Martin constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-04T06:57:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A63",
      "68R15",
      "11Y60",
      "11B85"
    ],
    "keywords": [
      "thue-morse sequence",
      "transcendental infinite products",
      "infinite product identities",
      "algebraic irrational",
      "flajolet-martin constant"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}