{
  "id": "1303.3122",
  "version": "v1",
  "published": "2013-03-13T10:17:47.000Z",
  "updated": "2013-03-13T10:17:47.000Z",
  "title": "Integral representations of the weighted geometric mean and the logarithmic mean",
  "authors": [
    "Feng Qi",
    "Xiao-Jing Zhang",
    "Wen-Hui Li"
  ],
  "comment": "12 pages. arXiv admin note: text overlap with arXiv:1301.6848",
  "journal": "Feng Qi, Xiao-Jing Zhang, and Wen-Hui Li, L\\'evy-Khintchine representations of the weighted geometric mean and the logarithmic mean, Mediterranean Journal of Mathematics 11 (2014), no. 2, 315--327",
  "doi": "10.1007/s00009-013-0311-z",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "In the paper, the authors show that the weighted geometric mean and the logarithmic mean are Bernstein functions and establish integral representations of these means by Cauchy's integral theorem in the theory of complex functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-13T10:17:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26E60",
      "30E20",
      "26A48",
      "44A20"
    ],
    "keywords": [
      "weighted geometric mean",
      "logarithmic mean",
      "cauchys integral theorem",
      "complex functions",
      "bernstein functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.3122Q"
    }
  }
}