{
  "id": "2104.00957",
  "version": "v1",
  "published": "2021-04-02T09:46:15.000Z",
  "updated": "2021-04-02T09:46:15.000Z",
  "title": "A note on some infinite sums of Hurwitz zeta functions",
  "authors": [
    "R B Paris"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "We consider some closed-form evaluations of certain infinite sums involving the Hurwitz zeta function $\\zeta(s,\\alpha)$ of the form \\[\\sum_{k=1}^\\infty (\\pm 1)^k k^m \\zeta(s,k),\\] where $m$ is a non-negative integer. For the sums with $m=0$ and the argument $k$ in $\\zeta(s,k)$ replaced by $ka+b$, where $a$ and $b$ are positive parameters, we also obtain a transformation formula suitable for computation in the limit $a\\to0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-02T09:46:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M35",
      "33E20"
    ],
    "keywords": [
      "hurwitz zeta function",
      "infinite sums",
      "closed-form evaluations",
      "positive parameters",
      "non-negative integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}