{
  "id": "1302.1986",
  "version": "v2",
  "published": "2013-02-08T10:36:02.000Z",
  "updated": "2013-02-11T08:07:00.000Z",
  "title": "Method for solving an iterative functional equation $A^{2^n}(x)=F(x)$",
  "authors": [
    "Dmitry Kruchinin",
    "Vladimir Kruchinin"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO",
    "math.CA",
    "math.FA",
    "math.NT"
  ],
  "abstract": "Using the notion of the composita, we obtain a method of solving iterative functional equations of the form $A^{2^n}(x)=F(x)$, where $F(x)=\\sum_{n>0} f(n)x^n$, $f(1)\\neq 0$. We prove that if $F(x)=\\sum_{n>0} f(n)x^n$ has integer coefficients, then the generating function $A(x)=\\sum_{n>0}a(n)x^n$, which is obtained from the iterative functional equation $4A(A(x))=F(4x)$, has integer coefficients. Key words: iterative functional equation, composition of generating functions, composita.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-11T08:07:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39B12"
    ],
    "keywords": [
      "integer coefficients",
      "generating function",
      "solving iterative functional equations",
      "composition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}