{
  "id": "1105.5770",
  "version": "v3",
  "published": "2011-05-29T09:43:32.000Z",
  "updated": "2013-07-26T05:43:01.000Z",
  "title": "A Connection Formula for the $q$-Confluent Hypergeometric Function",
  "authors": [
    "Takeshi Morita"
  ],
  "journal": "SIGMA 9 (2013), 050, 13 pages",
  "doi": "10.3842/SIGMA.2013.050",
  "categories": [
    "math.CA"
  ],
  "abstract": "We show a connection formula for the $q$-confluent hypergeometric functions ${}_2\\varphi_1(a,b;0;q,x)$. Combining our connection formula with Zhang's connection formula for ${}_2\\varphi_0(a,b;-;q,x)$, we obtain the connection formula for the $q$-confluent hypergeometric equation in the matrix form. Also we obtain the connection formula of Kummer's confluent hypergeometric functions by taking the limit $q\\to 1^{-}$ of our connection formula.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-07-26T05:43:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D15",
      "34M40",
      "39A13"
    ],
    "keywords": [
      "kummers confluent hypergeometric functions",
      "zhangs connection formula",
      "confluent hypergeometric equation",
      "matrix form"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2013,
      "month": "Jul",
      "volume": 9,
      "pages": "050"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013SIGMA...9..050M"
    }
  }
}