The power series $\displaystyle\sum^{∞}_{n=0}n!z^n$ and holomorphic solutions of some differential equations in a Banach space - Gefter, S. L.; Mokrenyuk, V .N. (Журнал математичної фізики, аналізу, геометрії, 2005)
Let $A$ be a bounded operator on a Banach space. A question about the existence of holomorphic solutions of the equation $z^2Aw'+g(z)=w$ is studied. Moreover, general properties of power series of the form $\displaystyle\sum^{∞}_{n=0}c_nA^nz^n$, $c_n\in \mathbb{C}$ are considered. Mathematics Subject Classification: 34A20, 34A25, 34G10.