{
  "id": "math/0010162",
  "version": "v1",
  "published": "2000-10-16T21:18:25.000Z",
  "updated": "2000-10-16T21:18:25.000Z",
  "title": "A new A_n extension of Ramanujan's 1-psi-1 summation with applications to multilateral A_n series",
  "authors": [
    "S. C. Milne",
    "M. Schlosser"
  ],
  "comment": "LaTeX2e, 26 pages, submitted to Rocky Mount. J. Math., spec. vol., conference proceedings of SF2000, Tempe, Arizona, May 29 - June 9, 2000",
  "categories": [
    "math.CA",
    "math.CO",
    "math.QA"
  ],
  "abstract": "In this article, we derive some identities for multilateral basic hypergeometric series associated to the root system A_n. First, we apply Ismail's argument to an A_n q-binomial theorem of Milne and derive a new A_n generalization of Ramanujan's 1-psi-1 summation theorem. From this new A_n 1-psi-1 summation and from an A_n 1-psi-1 summation of Gustafson we deduce two lemmas for deriving simple A_n generalizations of bilateral basic hypergeometric series identities. These lemmas are closely related to the Macdonald identities for A_n. As samples for possible applications of these lemmas, we provide several A_n extensions of Bailey's 2-psi-2 transformations, and several A_n extensions of a particular 2-psi-2 summation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-10-16T21:18:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D15",
      "05A19",
      "33D67"
    ],
    "keywords": [
      "applications",
      "ramanujans",
      "bilateral basic hypergeometric series identities",
      "multilateral basic hypergeometric series",
      "generalization"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....10162M"
    }
  }
}