{
  "id": "1812.04467",
  "version": "v1",
  "published": "2018-12-11T15:30:03.000Z",
  "updated": "2018-12-11T15:30:03.000Z",
  "title": "$q$-Difference Equations and Identities of the Rogers--Ramanujan--Bailey Type",
  "authors": [
    "Andrew V. Sills"
  ],
  "comment": "14 pages",
  "journal": "Journal of Difference Equations and Applications Vol. 10, No. 12, October 2004, pp. 1069--1084",
  "doi": "10.1080/10236190412331314169",
  "categories": [
    "math.CA"
  ],
  "abstract": "In a recent paper, I defined the \"standard multiparameter Bailey pair\" (SMPBP) and demonstrated that all of the classical Bailey pairs considered by W.N. Bailey in his famous paper (\\textit{Proc. London Math. Soc. (2)}, \\textbf{50} (1948), 1--10) arose as special cases of the SMPBP. Additionally, I was able to find a number of new Rogers-Ramanujan type identities. From a given Bailey pair, normally only one or two Rogers-Ramanujan type identities follow immediately. In this present work, I present the set of $q$-difference equations associated with the SMPBP, and use these $q$-difference equations to deduce the complete families of Rogers-Ramanujan type identities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-11T15:30:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B65",
      "39A13",
      "05A19",
      "33D15"
    ],
    "keywords": [
      "difference equations",
      "rogers-ramanujan type identities",
      "rogers-ramanujan-bailey type",
      "standard multiparameter bailey pair",
      "classical bailey pairs"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Taylor-Francis"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}