{
  "id": "0901.0249",
  "version": "v1",
  "published": "2009-01-02T16:31:34.000Z",
  "updated": "2009-01-02T16:31:34.000Z",
  "title": "On the q-Extensions of the Bernoulli and Euler Numbers, Related Identities and Lerch Zeta Function",
  "authors": [
    "Taekyun Kim",
    "Younghee Kim",
    "kyoungwon Hwang"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Recently, $\\lambda$-Bernoulli and $\\lambda$-Euler numbers are studied in [5, 10]. The purpose of this paper is to present a systematic study of some families of the $q$-extensions of the $\\lambda$-Bernoulli and the $\\lambda$-Euler numbers by using the bosonic $p$-adic $q$-integral and the fermionic $p$-adic $q$-integral. The investigation of these $\\lambda$-$q$-Bernoulli and $\\lambda$-$q$-Euler numbers leads to interesting identities related to these objects. The results of the present paper cover earlier results concerning $q$-Bernoulli and $q$-Euler numbers. By using derivative operator to the generating functions of $\\lambda$-$q$-Bernoulli and $\\lambda$-$q$-Euler numbers, we give the $q$-extensions of Lerch zeta function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-02T16:31:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B68",
      "11S80"
    ],
    "keywords": [
      "euler numbers",
      "lerch zeta function",
      "related identities",
      "q-extensions",
      "paper cover earlier results concerning"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0901.0249K"
    }
  }
}