Method for solving an iterative functional equation $A^{2^n}(x)=F(x)$
| Autor: | Kruchinin, Dmitry, Kruchinin, Vladimir |
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| Rok vydání: | 2013 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 11 pages |
| Databáze: | arXiv |
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