{
  "id": "2302.14199",
  "version": "v1",
  "published": "2023-02-27T23:30:51.000Z",
  "updated": "2023-02-27T23:30:51.000Z",
  "title": "On ${}_5ψ_5$ identities of Bailey",
  "authors": [
    "Aritram Dhar"
  ],
  "comment": "10 pages. Comments are welcome!",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "In this paper, we provide proofs of two ${}_5\\psi_5$ summation formulas of Bailey using a ${}_5\\phi_4$ identity of Carlitz. We show that in the limiting case, the two ${}_5\\psi_5$ identities give rise to two ${}_3\\psi_3$ summation formulas of Bailey. Finally, we prove the two ${}_3\\psi_3$ identities using a technique initially used by Ismail to prove Ramanujan's ${}_1\\psi_1$ summation formula and later by Ismail and Askey to prove Bailey's very-well-poised ${}_6\\psi_6$ sum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-27T23:30:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D15",
      "33D65"
    ],
    "keywords": [
      "summation formula",
      "limiting case",
      "ramanujans"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}