On Composition of Formal Power Series
نویسندگان
چکیده
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.
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