{
  "id": "math/0203264",
  "version": "v4",
  "published": "2002-03-26T00:20:17.000Z",
  "updated": "2004-08-23T22:17:01.000Z",
  "title": "On reducing the Heun equation to the hypergeometric equation",
  "authors": [
    "Robert S. Maier"
  ],
  "comment": "36 pages, a few additional misprints corrected",
  "journal": "J. Differential Equations 213 (2005) 171-203",
  "doi": "10.1016/j.jde.2004.07.020",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The reductions of the Heun equation to the hypergeometric equation by polynomial transformations of its independent variable are enumerated and classified. Heun-to-hypergeometric reductions are similar to classical hypergeometric identities, but the conditions for the existence of a reduction involve features of the Heun equation that the hypergeometric equation does not possess; namely, its cross-ratio and accessory parameters. The reductions include quadratic and cubic transformations, which may be performed only if the singular points of the Heun equation form a harmonic or an equianharmonic quadruple, respectively; and several higher-degree transformations. This result corrects and extends a theorem in a previous paper, which found only the quadratic transformations. [See K. Kuiken, \"Heun's equation and the hypergeometric equation\", SIAM Journal on Mathematical Analysis 10:3 (1979), 655-657.]",
  "revisions": [
    {
      "version": "v4",
      "updated": "2004-08-23T22:17:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33E30",
      "34M35",
      "33C05"
    ],
    "keywords": [
      "hypergeometric equation",
      "heun equation form",
      "polynomial transformations",
      "accessory parameters",
      "heun-to-hypergeometric reductions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......3264M"
    }
  }
}