{
  "id": "1912.01199",
  "version": "v1",
  "published": "2019-12-03T05:39:31.000Z",
  "updated": "2019-12-03T05:39:31.000Z",
  "title": "On Hurwitz zeta function and Lommel functions",
  "authors": [
    "Atul Dixit",
    "Rahul Kumar"
  ],
  "comment": "9 pages, submitted for publication",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "We obtain a new proof of Hurwitz's formula for the Hurwitz zeta function $\\zeta(s, a)$ beginning with Hermite's formula. The aim is to reveal a nice connection between $\\zeta(s, a)$ and a special case of the Lommel function $S_{\\mu, \\nu}(z)$. This connection is used to rephrase a modular-type transformation involving infinite series of Hurwitz zeta function in terms of those involving Lommel functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-03T05:39:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M35",
      "33C10",
      "33C47"
    ],
    "keywords": [
      "hurwitz zeta function",
      "lommel function",
      "infinite series",
      "hurwitzs formula",
      "nice connection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}