On composition of formal power series
| Autor: | Xiao-Xiong Gan, Nathaniel Knox |
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| Jazyk: | angličtina |
| Rok vydání: | 2002 |
| Předmět: | |
| Zdroj: | International Journal of Mathematics and Mathematical Sciences, Vol 30, Iss 12, Pp 761-770 (2002) |
| Druh dokumentu: | article |
| ISSN: | 0161-1712 1687-0425 01611712 |
| DOI: | 10.1155/S0161171202107150 |
| Popis: | Given a formal power series g(x)=b0+b1x+b2x2+⋯ and a nonunit f(x)=a1x+a2x2+⋯, it is well known that the composition of g with f, g(f(x)), is a formal power series. If the formal power series f above is not a nonunit, that is, the constant term of f is not zero, the existence of the composition g(f(x)) has been an open problem for many years. The recent development investigated the radius of convergence of a composed formal power series like f above and obtained some very good results. This note gives a necessary and sufficient condition for the existence of the composition of some formal power series. By means of the theorems established in this note, the existence of the composition of a nonunit formal power series is a special case. |
| Databáze: | Directory of Open Access Journals |
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