{
  "id": "1603.00722",
  "version": "v1",
  "published": "2016-03-02T14:33:24.000Z",
  "updated": "2016-03-02T14:33:24.000Z",
  "title": "Integrals of products of Hurwitz zeta functions",
  "authors": [
    "M. A. Shpot",
    "M. P. Chaudhary",
    "R. B. Paris"
  ],
  "categories": [
    "math.CA",
    "hep-th",
    "math.CV"
  ],
  "abstract": "We evaluate two integrals over $x\\in [0,1]$ involving products of the function $\\zeta_1(a,x)\\equiv \\zeta(a,x)-x^{-a}$ for $\\Re (a)>1$, where $\\zeta(a,x)$ is the Hurwitz zeta function. The evaluation of these integrals for the particular case of integer $a\\geq 2$ is also presented. As an application we calculate the $O(g)$ weak-coupling expansion coefficient $c_{1}(\\varepsilon)$ of the Casimir energy for a film with Dirichlet-Dirichlet boundary conditions, first stated by Symanzik [Schr\\\"odinger representation and Casimir effect in renormalizable quantum field theory, Nucl. Phys. B 190 (1981) 1-44] in the framework of $g\\phi^4_{4-\\varepsilon}$ theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-02T14:33:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M35",
      "11B68",
      "33B15",
      "33E20"
    ],
    "keywords": [
      "hurwitz zeta function",
      "dirichlet-dirichlet boundary conditions",
      "renormalizable quantum field theory",
      "casimir effect",
      "casimir energy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160300722S",
      "inspire": 1425709
    }
  }
}