{
  "id": "1904.07808",
  "version": "v1",
  "published": "2019-04-15T14:34:10.000Z",
  "updated": "2019-04-15T14:34:10.000Z",
  "title": "An Asymptotic Form of the Generating Function $\\prod_{k=1}^\\infty (1+x^k/k)$",
  "authors": [
    "Andreas B. G. Blobel"
  ],
  "comment": "9 pages, 1 figure",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "It is shown that the sequence of rational numbers $r(k)$ generated by the ordinary generating function $\\prod_{k=1}^\\infty (1+x^k/k)$ converges to a limit $C > 0$. $C$ can be expressed as $C = \\exp\\Bigl(-\\sum_{k = 2}^\\infty \\frac{(-1)^k}{k}\\ \\zeta(k) \\Bigr)$ where $\\zeta()$ denotes the Riemann zeta function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-15T14:34:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic form",
      "riemann zeta function",
      "rational numbers",
      "ordinary generating function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}