Julia directions of meromorphic functions and their derivatives

Abstract.

We prove that if a transcendental meromorphic function has no Julia direction and is bounded on a path to \( \infty \) then there is a common Julia direction for all derivatives. Related statements are obtained under the assumption that f is \( o(\sqrt{\mid z \mid}) \) or \( O(\sqrt{\mid z \mid}) \) on a path to \( \infty \). Further we disprove a conjecture of Frank and Wang by means of a counterexample.