{
  "id": "1903.09228",
  "version": "v1",
  "published": "2019-03-21T20:27:04.000Z",
  "updated": "2019-03-21T20:27:04.000Z",
  "title": "Bernoulli and Euler numbers from divergent series",
  "authors": [
    "Sergio A. Carrillo"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "The aim of this note is to provide a simple proof of some well-known identities and recurrences relating classical Bernoulli and Euler numbers by using the Abel sum of the divergent series $\\sum_{n=0}^\\infty (-1)^{n} (n+1)^k$, $k$ a positive integers. Special attention is placed on the fact that the numerical value of these sums is determined by the linearity of the summation method involved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-21T20:27:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B68",
      "40G10"
    ],
    "keywords": [
      "divergent series",
      "euler numbers",
      "summation method",
      "recurrences relating classical bernoulli",
      "simple proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}