{
  "id": "2308.06800",
  "version": "v1",
  "published": "2023-08-13T15:54:52.000Z",
  "updated": "2023-08-13T15:54:52.000Z",
  "title": "Some q-Identities derived by the ordinary derivative operator",
  "authors": [
    "Jin Wang",
    "Ruiqi Ruan",
    "Xinrong Ma"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we investigate applications of the ordinary derivative operator, instead of the $q$-derivative operator, to the theory of $q$-series. As main results, many new summation and transformation formulas are established which are closely related to some well-known formulas such as the $q$-binomial theorem, Ramanujan's ${}_1\\psi_1$ formula, the quintuple product identity, Gasper's $q$-Clausen product formula, and Rogers' ${}_6\\phi_5$ formula, etc. Among these results is a finite form of the Rogers-Ramanujan identity and a short way to Eisenstein's theorem on Lambert series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-13T15:54:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A30",
      "33D15"
    ],
    "keywords": [
      "ordinary derivative operator",
      "q-identities",
      "clausen product formula",
      "quintuple product identity",
      "finite form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}