Geodesic
Further remarks on formal power series
Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 4, pp. 549-555.

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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.
Classification : 13F25, 13J05
Keywords: formal power series; superposition; boundary convergence 
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Borkowski, Marcin; Maćkowiak, Piotr. Further remarks on formal power series. Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 4, pp. 549-555. http://geodesic.mathdoc.fr/item/CMUC_2012__53_4_a3/