{
  "id": "2206.15434",
  "version": "v1",
  "published": "2022-06-30T17:27:34.000Z",
  "updated": "2022-06-30T17:27:34.000Z",
  "title": "A simple algorithm for expanding a power series as a continued fraction",
  "authors": [
    "Alan D. Sokal"
  ],
  "comment": "LaTeX2e, 47 pages",
  "categories": [
    "math.CO",
    "math.CA",
    "math.CV"
  ],
  "abstract": "I present and discuss an extremely simple algorithm for expanding a formal power series as a continued fraction. This algorithm, which goes back to Euler (1746) and Viscovatov (1805), deserves to be better known. I also discuss the connection of this algorithm with the work of Gauss (1812), Stieltjes (1889), Rogers (1907) and Ramanujan, and a combinatorial interpretation based on the work of Flajolet (1980).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-30T17:27:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30B70",
      "05A10",
      "05A15",
      "05A19"
    ],
    "keywords": [
      "continued fraction",
      "formal power series",
      "extremely simple algorithm",
      "combinatorial interpretation",
      "viscovatov"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}