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.
 Bugajewski D., Gan X.-X.: A note on formal power series
. Comment. Math. Univ. Carolin. 51 (2010), no. 4, 595–604. MR 2858263
| Zbl 1224.13025