{
  "id": "1602.04359",
  "version": "v1",
  "published": "2016-02-13T17:28:51.000Z",
  "updated": "2016-02-13T17:28:51.000Z",
  "title": "Log-behavior of two sequences related to the elliptic integrals",
  "authors": [
    "Brian Y. Sun",
    "James J. Y. Zhao"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Two interesting sequences arose in the study of the series expansions of the complete elliptic integrals, which are called the Catalan-Larcombe-French sequence $\\{P_n\\}_{n\\geq 0}$ and the Fennessey-Larcombe-French sequence $\\{V_n\\}_{n\\geq 0}$ respectively. In this paper, we prove the ratio log-concavity of $\\{P_n\\}_{n\\geq 0}$, the log-convexity of $\\{V_n^2-V_{n-1}V_{n+1}\\}_{n\\geq 2}$, the ratio log-convexity of $\\{V_n\\}_{n\\geq 1}$, and the log-convexity of $\\{n!V_n\\}_{n\\geq 1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-13T17:28:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A20"
    ],
    "keywords": [
      "log-behavior",
      "complete elliptic integrals",
      "ratio log-concavity",
      "fennessey-larcombe-french sequence",
      "series expansions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160204359S"
    }
  }
}