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.
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Eingegangen am 19. 10. 2000
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Sauer, A. Julia directions of meromorphic functions and their derivatives. Arch. Math. 79, 182–187 (2002). https://doi.org/10.1007/s00013-002-8303-4
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DOI: https://doi.org/10.1007/s00013-002-8303-4