on composition of formal power series
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ID: 202403
2002
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Abstract
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.
| Reference Key |
gan2002internationalon
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| Authors | ;Xiao-Xiong Gan;Nathaniel Knox |
| Journal | structural engineering and mechanics |
| Year | 2002 |
| DOI |
10.1155/S0161171202107150
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| URL | |
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