{
  "id": "1202.2006",
  "version": "v1",
  "published": "2012-02-09T14:49:21.000Z",
  "updated": "2012-02-09T14:49:21.000Z",
  "title": "Eight interesting identities involving the exponential function, derivatives, and Stirling numbers of the second kind",
  "authors": [
    "Feng Qi"
  ],
  "comment": "9 pages",
  "journal": "Bai-Ni Guo and Feng Qi, Some identities and an explicit formula for Bernoulli and Stirling numbers, Journal of Computational and Applied Mathematics 255 (2014), 568--579",
  "doi": "10.1016/j.cam.2013.06.020",
  "categories": [
    "math.CA",
    "math.CO",
    "math.NT"
  ],
  "abstract": "In the paper, the author establishes some identities which show that the functions $\\frac1{(1-e^{\\pm t})^k}$ and the derivatives $\\bigl(\\frac1{e^{\\pm t}-1}\\bigr)^{(i)}$ can be expressed each other by linear combinations with coefficients involving the combinatorial numbers and the Stirling numbers of the second kind, where $t\\ne0$ and $i,k\\in\\mathbb{N}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-09T14:49:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A24",
      "33B10",
      "11B73",
      "34A30"
    ],
    "keywords": [
      "second kind",
      "stirling numbers",
      "exponential function",
      "interesting identities",
      "derivatives"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.2006Q"
    }
  }
}