{
  "id": "2409.06878",
  "version": "v1",
  "published": "2024-09-10T21:47:17.000Z",
  "updated": "2024-09-10T21:47:17.000Z",
  "title": "Deformed Homogeneous $(s,t)$-Rogers-Szegö Polynomials and the Deformed $(s,t)$-Exponential Operator e$_{s,t}(y{\\rm T}_a D_{s,t},v)$",
  "authors": [
    "Ronald Orozco López"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "This article introduces the deformed homogeneous $(s,t)$-Rogers-Szeg\\\"o polynomials h$_{n}(x,y;s,t,u,v)$. These polynomials are a generalization of the Rogers-Szeg\\\"o polynomials and the $(p,q)$-Rogers-Szeg\\\"o polynomials defined by Jagannathan. By using the deformed $(s,t)$-exponential operator based on operator T$_{a}D_{s,t}$ we find identities involving the polynomials h$_{n}(x,y;s,t,u,v)$, together with generalizations of the Mehler and Rogers formulas. In addition, a generating function for the polynomials h$_{n}(x,y;s,t,u,v)$ is found employing the deformed $\\frac{\\varphi}{u}$-commuting operators. A representation of deformed $(s,t)$-exponential function as the limit of a sequence of deformed $(s,t)$-Rogers-Szeg\\\"o polynomials is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-10T21:47:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A30",
      "11B39",
      "33D15",
      "33D45"
    ],
    "keywords": [
      "polynomials",
      "exponential operator",
      "deformed homogeneous",
      "generalization",
      "rogers formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}