{
  "id": "0903.3071",
  "version": "v1",
  "published": "2009-03-18T01:28:45.000Z",
  "updated": "2009-03-18T01:28:45.000Z",
  "title": "Necessary and sufficient conditions for a function involving divided differences of the di- and tri-gamma functions to be completely monotonic",
  "authors": [
    "Feng Qi",
    "Bai-Ni Guo"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "In the present paper, necessary and sufficient conditions are established for a function involving divided differences of the digamma and trigamma functions to be completely monotonic. Consequently, necessary and sufficient conditions are derived for a function involving the ratio of two gamma functions to be logarithmically completely monotonic, and some double inequalities are deduced for bounding divided differences of polygamma functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-18T01:28:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A48",
      "33B15",
      "26A51",
      "26D10",
      "65R10"
    ],
    "keywords": [
      "sufficient conditions",
      "tri-gamma functions",
      "polygamma functions",
      "trigamma functions",
      "double inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.3071Q"
    }
  }
}