{
  "id": "1504.03255",
  "version": "v1",
  "published": "2015-04-13T16:57:04.000Z",
  "updated": "2015-04-13T16:57:04.000Z",
  "title": "The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case",
  "authors": [
    "Luise Adams",
    "Christian Bogner",
    "Stefan Weinzierl"
  ],
  "comment": "31 pages",
  "categories": [
    "hep-ph",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We present the result for the finite part of the two-loop sunrise integral with unequal masses in four space-time dimensions in terms of the ${\\mathcal O}(\\varepsilon^0)$-part and the ${\\mathcal O}(\\varepsilon^1)$-part of the sunrise integral around two space-time dimensions. The latter two integrals are given in terms of elliptic generalisations of Clausen and Glaisher functions. Interesting aspects of the result for the ${\\mathcal O}(\\varepsilon^1)$-part of the sunrise integral around two space-time dimensions are the occurrence of depth two elliptic objects and the weights of the individual terms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-13T16:57:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-loop sunrise integral",
      "space-time dimensions",
      "glaisher functions",
      "elliptic case",
      "finite part"
    ],
    "publication": {
      "doi": "10.1063/1.4926985"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1359312
    }
  }
}