{
  "id": "1911.05883",
  "version": "v1",
  "published": "2019-11-14T01:19:19.000Z",
  "updated": "2019-11-14T01:19:19.000Z",
  "title": "A ratio of many gamma functions and its properties with applications",
  "authors": [
    "Feng Qi",
    "Wen-Hui Li",
    "Shu-Bin Yu",
    "Xin-Yu Du",
    "Bai-Ni Guo"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CA",
    "math.CO"
  ],
  "abstract": "In the paper, the authors establish an inequality involving exponential functions and sums, introduce a ratio of many gamma functions, discuss properties, including monotonicity, logarithmic convexity, (logarithmically) complete monotonicity, and the Bernstein function property, of the newly introduced ratio, and construct two inequalities of multinomial coefficients and multivariate beta functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-14T01:19:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A48",
      "05A20",
      "26D07",
      "26A51",
      "26D15",
      "33B15",
      "44A10"
    ],
    "keywords": [
      "gamma functions",
      "applications",
      "multivariate beta functions",
      "bernstein function property",
      "exponential functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}