{
  "id": "1609.05658",
  "version": "v1",
  "published": "2016-09-19T10:31:16.000Z",
  "updated": "2016-09-19T10:31:16.000Z",
  "title": "Integrals of products of Hurwitz zeta functions via Feynman parametrization and two double sums of Riemann zeta functions",
  "authors": [
    "M. A. Shpot",
    "R. B. Paris"
  ],
  "comment": "14 pages 0 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "We consider two integrals over $x\\in [0,1]$ involving products of the function $\\zeta_1(a,x)\\equiv \\zeta(a,x)-x^{-a}$, where $\\zeta(a,x)$ is the Hurwitz zeta function, given by $$\\int_0^1\\zeta_1(a,x)\\zeta_1(b,x)\\,dx\\quad\\mbox{and}\\quad \\int_0^1\\zeta_1(a,x)\\zeta_1(b,1-x)\\,dx$$ when $\\Re (a,b)>1$. These integrals have been investigated recently in \\cite{SCP}; here we provide an alternative derivation by application of Feynman parametrization. We also discuss a moment integral and the evaluation of two doubly infinite sums containing the Riemann zeta function $\\zeta(x)$ and two free parameters $a$ and $b$. The limiting forms of these sums when $a+b$ takes on integer values are considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-19T10:31:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M35",
      "33B15",
      "33E20"
    ],
    "keywords": [
      "riemann zeta function",
      "hurwitz zeta function",
      "feynman parametrization",
      "double sums",
      "moment integral"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}