{
  "id": "1709.03398",
  "version": "v1",
  "published": "2017-09-11T14:22:10.000Z",
  "updated": "2017-09-11T14:22:10.000Z",
  "title": "More Infinite Products: Thue-Morse and the Gamma function",
  "authors": [
    "Jean-Paul Allouche",
    "Samin Riasat",
    "Jeff Shallit"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Letting $(t_n)$ denote the Thue-Morse sequence with values $0, 1$, we note that the Woods-Robbins product $$ \\prod_{n \\geq 0} \\left(\\frac{2n+1}{2n+2}\\right)^{(-1)^{t_n}} = 2^{-1/2} $$ involves a rational function in $n$ and the $\\pm 1$ Thue-Morse sequence $((-1)^{t_n})_{n \\geq 0}$. The purpose of this paper is twofold. On the one hand, we try to find other rational functions for which similar infinite products involving the $\\pm 1$ Thue-Morse sequence have an expression in terms of known constants. On the other hand, we also try to find (possibly different) rational functions $R$ for which the infinite product $\\prod R(n)^{t_n}$ also has an expression in terms of known constants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-11T14:22:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A63",
      "11B83",
      "11B85",
      "68R15"
    ],
    "keywords": [
      "gamma function",
      "thue-morse sequence",
      "rational function",
      "similar infinite products",
      "woods-robbins product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}