{
  "id": "1609.09336",
  "version": "v1",
  "published": "2016-09-29T13:43:26.000Z",
  "updated": "2016-09-29T13:43:26.000Z",
  "title": "On the integral of products of higher-order Bernoulli and Euler polynomials",
  "authors": [
    "M. Cihat Dagli",
    "Mümün Can"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we derive a formula on the integral of products of the higher-order Euler polynomials. By the same way, similar relations are obtained for $l$ higher-order Bernoulli polynomials and $r$ higher-order Euler polynomials. Moreover, we establish the connection between the results and the generalized Dedekind sums and Hardy--Berndt sums. Finally, the Laplace transform of Euler polynomials is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-29T13:43:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B68",
      "11F20"
    ],
    "keywords": [
      "higher-order euler polynomials",
      "higher-order bernoulli polynomials",
      "laplace transform",
      "generalized dedekind sums",
      "hardy-berndt sums"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}