{
  "id": "1812.10878",
  "version": "v1",
  "published": "2018-12-28T03:11:00.000Z",
  "updated": "2018-12-28T03:11:00.000Z",
  "title": "A Theorem on Divergence in the General Sense for Continued Fractions",
  "authors": [
    "Douglas Bowman",
    "James Mc Laughlin"
  ],
  "comment": "11 pages",
  "journal": "The Journal of Computational and Applied Mathematics 172, (2004) no. 2, pp 363--373",
  "doi": "10.1016/j.cam.2004.02.012",
  "categories": [
    "math.NT"
  ],
  "abstract": "If the odd and even parts of a continued fraction converge to different values, the continued fraction may or may not converge in the general sense. We prove a theorem which settles the question of general convergence for a wide class of such continued fractions. We apply this theorem to two general classes of $q$ continued fraction to show, that if $G(q)$ is one of these continued fractions and $|q|>1$, then either $G(q)$ converges or does not converge in the general sense. We also show that if the odd and even parts of the continued fraction $K_{n=1}^{\\infty}a_{n}/1$ converge to different values, then $\\lim_{n \\to \\infty}|a_{n}| = \\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-28T03:11:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A55"
    ],
    "keywords": [
      "general sense",
      "divergence",
      "continued fraction converge",
      "general classes",
      "wide class"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}