{
  "id": "0903.5123",
  "version": "v1",
  "published": "2009-03-30T04:02:52.000Z",
  "updated": "2009-03-30T04:02:52.000Z",
  "title": "Some logarithmically completely monotonic functions related to the gamma function",
  "authors": [
    "Feng Qi",
    "Bai-Ni Guo"
  ],
  "comment": "16 pages",
  "journal": "Feng Qi and Bai-Ni Guo, Some logarithmically completely monotonic functions related to the gamma function, Journal of the Korean Mathematical Society 47 (2010), no. 6, 1283--1297",
  "doi": "10.4134/JKMS.2010.47.6.1283",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this article, logarithmically complete monotonicity properties of some functions such as $\\frac1{[\\Gamma(x+1)]^{1/x}}$, $\\frac{[{\\Gamma(x+\\alpha+1)}]^{1/(x+\\alpha)}}{[{\\Gamma(x+1)}]^{1/x}}$, $\\frac{[\\Gamma(x+1)]^{1/x}}{(x+1)^\\alpha}$ and $\\frac{[\\Gamma(x+1)]^{1/x}}{x^\\alpha}$ defined in $(-1,\\infty)$ or $(0,\\infty)$ for given real number $\\alpha\\in\\tr$ are obtained, some known results are recovered, extended and generalized. Moreover, some basic properties of the logarithmically completely monotonic functions are established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-30T04:02:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33B15",
      "65R10",
      "26A48",
      "26A51"
    ],
    "keywords": [
      "monotonic functions",
      "gamma function",
      "logarithmically complete monotonicity properties",
      "basic properties",
      "real number"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.5123Q"
    }
  }
}