{
  "id": "1909.00058",
  "version": "v1",
  "published": "2019-08-29T13:35:22.000Z",
  "updated": "2019-08-29T13:35:22.000Z",
  "title": "Can Umbral and $q$-calculus be merged?",
  "authors": [
    "G. Dattoli",
    "B. Germano",
    "K. Górska",
    "M. R. Martinelli"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "The $q$-calculus is reformulated in terms of the umbral calculus and of the associated operational formalism. We show that new and interesting elements emerge from such a restyling. The proposed technique is applied to a different formulations of $q$ special functions, to the derivation of integrals involving ordinary and $q$-functions and to the study of $q$-special functions and polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-29T13:35:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "special functions",
      "associated operational formalism",
      "umbral calculus",
      "interesting elements emerge",
      "formulations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}