{
  "id": "2005.13515",
  "version": "v1",
  "published": "2020-05-26T15:36:03.000Z",
  "updated": "2020-05-26T15:36:03.000Z",
  "title": "An analytic generalization of the Catalan numbers and its integral representation",
  "authors": [
    "Feng Qi",
    "Wen-Hui Li",
    "Jian Cao",
    "Da-Wei Niu",
    "Jiao-Lian Zhao"
  ],
  "comment": "14 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "In the paper, the authors analytically generalize the Catalan numbers in combinatorial number theory, establish an integral representation of the analytic generalization of the Catalan numbers by virtue of Cauchy's integral formula in the theory of complex functions, and point out potential directions to further study.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-26T15:36:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "11B75",
      "11B83",
      "26A09",
      "30E20",
      "41A58"
    ],
    "keywords": [
      "catalan numbers",
      "integral representation",
      "analytic generalization",
      "combinatorial number theory",
      "cauchys integral formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}