{
  "id": "1104.4442",
  "version": "v1",
  "published": "2011-04-22T14:01:38.000Z",
  "updated": "2011-04-22T14:01:38.000Z",
  "title": "Complete monotonicity of a function involving the gamma function and applications",
  "authors": [
    "Feng Qi"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "In the article we present necessary and sufficient conditions for a function involving the logarithm of the gamma function to be completely monotonic and apply these results to bound the gamma function $\\Gamma(x)$, the $n$-th harmonic number $\\sum_{k=1}^n\\frac1k$, and the factorial $n!$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-22T14:01:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A48",
      "33B15",
      "26D15"
    ],
    "keywords": [
      "gamma function",
      "complete monotonicity",
      "applications",
      "th harmonic number",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.4442Q"
    }
  }
}