{
  "id": "1906.04579",
  "version": "v1",
  "published": "2019-06-09T13:48:48.000Z",
  "updated": "2019-06-09T13:48:48.000Z",
  "title": "Viète's formulas for zeros of solutions of Schröder-Poincaré functional equations",
  "authors": [
    "A. A. Kutsenko"
  ],
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "Solutions of Schr\\\"oder-Poincar\\'e's polynomial equations $f(az)=P(f(z))$ usually do not admit a simple closed form representation in terms of known standard functions. We show that there is a one-to-one correspondence between zeros of $f$ and a set of discrete functions stable at infinity. The corresponding Vi\\`ete-type infinite product expansions for zeros of $f$ are also provided. This allows us to obtain a special kind of closed-form representation for $f$ based on the Weierstrass-Hadamard expansion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-09T13:48:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "functional equations",
      "viètes formulas",
      "simple closed form representation",
      "infinite product expansions",
      "closed-form representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}