{
  "id": "1006.3336",
  "version": "v1",
  "published": "2010-06-16T22:42:33.000Z",
  "updated": "2010-06-16T22:42:33.000Z",
  "title": "Barnes multiple zeta-functions, Ramanujan's formula, and relevant series involving hyperbolic functions",
  "authors": [
    "Yasushi Komori",
    "Kohji Matsumoto",
    "Hirofumi Tsumura"
  ],
  "comment": "16 pages",
  "journal": "J. Ramanujan Math. Soc. 28 (2013), 49-69",
  "categories": [
    "math.NT"
  ],
  "abstract": "In the former part of this paper, we give functional equations for Barnes multiple zeta-functions and consider some relevant results. In particular, we show that Ramanujan's classical formula for the Riemann zeta values can be derived from functional equations for Barnes zeta-functions. In the latter half part, we generalize some evaluation formulas of certain series involving hyperbolic functions in terms of Bernoulli polynomials. The original formulas were classically given by Cauchy, Mellin, Ramanujan, and later recovered and formulated by Berndt. From our consideration, we give multiple versions of these known formulas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-16T22:42:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M41",
      "11B68"
    ],
    "keywords": [
      "barnes multiple zeta-functions",
      "hyperbolic functions",
      "relevant series",
      "ramanujans formula",
      "functional equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.3336K"
    }
  }
}