{
  "id": "1602.01384",
  "version": "v1",
  "published": "2016-02-03T17:37:59.000Z",
  "updated": "2016-02-03T17:37:59.000Z",
  "title": "Analytic Continuation of Hypergeometric Functions in the Resonant Case",
  "authors": [
    "Emanuel Scheidegger"
  ],
  "comment": "32 pages",
  "categories": [
    "math.CA",
    "hep-th",
    "math.AG",
    "math.CV"
  ],
  "abstract": "We perform the analytic continuation of solutions to the hypergeometric differential equation of order $n$ to the third regular singularity, usually denoted $z=1$, with the help of recurrences of their Mellin--Barnes integral representations. In the resonant case, there are necessarily logarithmic solutions. We apply the result to Picard-Fuchs equations of certain one--parameter families of Calabi--Yau manifolds, known as the mirror quartic and the mirror quintic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-03T17:37:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "resonant case",
      "analytic continuation",
      "hypergeometric functions",
      "third regular singularity",
      "hypergeometric differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160201384S",
      "inspire": 1419278
    }
  }
}