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Further remarks on formal power series

Marcin BorkowskiPiotr Maćkowiak — 2012

Commentationes Mathematicae Universitatis Carolinae

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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