{
  "id": "math/0103149",
  "version": "v1",
  "published": "2001-03-24T14:17:33.000Z",
  "updated": "2001-03-24T14:17:33.000Z",
  "title": "On a functional-difference equation of Runyon, Morrison, Carlitz, and Riordan",
  "authors": [
    "Helmut Prodinger"
  ],
  "comment": "Avoid recursions, use generating functions",
  "categories": [
    "math.CO"
  ],
  "abstract": "A certain functional-difference equation that Runyon encountered when analyzing a queuing system was solved in a combined effort of Morrison, Carlitz, and Riordan. We simplify that analysis by exclusively using generating functions, in particular the kernel method, and the Lagrange inversion formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-03-24T14:17:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "04A15"
    ],
    "keywords": [
      "functional-difference equation",
      "lagrange inversion formula",
      "kernel method",
      "queuing system",
      "generating functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......3149P"
    }
  }
}