{
  "id": "1508.07438",
  "version": "v1",
  "published": "2015-08-29T11:47:37.000Z",
  "updated": "2015-08-29T11:47:37.000Z",
  "title": "On the continued fraction expansion of certain Engel series",
  "authors": [
    "Andrew N. W. Hone"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "An Engel series is a sum of the reciprocals of an increasing sequence of positive integers, which is such that each term is divisible by the previous one. Here we consider a particular class of Engel series, for which each term of the sequence is divisible by the square of the preceding one, and find an explicit expression for the continued fraction expansion of the sum of a generic series of this kind. A family of examples generated by nonlinear recurrences with the Laurent property are considered in detail, along with some associated transcendental numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-29T11:47:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J70",
      "11B37"
    ],
    "keywords": [
      "continued fraction expansion",
      "engel series",
      "explicit expression",
      "generic series",
      "nonlinear recurrences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150807438H"
    }
  }
}