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formal power series; superposition; boundary convergence
In this paper, we present a considerable simplification of the proof of a theorem by Gan and Knox, stating a sufficient and necessary condition for existence of a composition of two formal power series. Then, we consider the behavior of such series and their (formal) derivatives at the boundary of the convergence circle, obtaining in particular a theorem of Bugajewski and Gan concerning the structure of the set of points where a formal power series is convergent with all its derivatives.
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[5] Lang S.: Complex Analysis. Springer, 4th edition, New York, 1999. MR 1659317 | Zbl 0933.30001
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