Given some positive constant $ R>0$ how can we characterize the set of all functions $ f(z)=\sum_{k=2}^\infty \frac{a_k}{k!}z^k$ analytic in $ |z|<R$ for which there exists $ C>0$ (same for all $ f$ from that set) such that $ $ |f(z)|\leq C|a_2|$ $ for $ |z|<R$ ? Does there exists such $ R$ for whichRead more