Abstract
We study the behaviour of the sequence of successive derivatives of meromorphic functions at points of the so-called final set. We prove that, whereas in many cases this sequence tends to ∞, for a special class of meromorphic functions, it may have extremely wild behaviour. We also prove a connection between the derivatives of meromorphic functions from this class and so-called Dirichlet sets.
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Meyrath, T., Müller, J. On the behaviour of the successive derivatives of meromorphic functions on the final set. JAMA 120, 131–149 (2013). https://doi.org/10.1007/s11854-013-0017-y
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DOI: https://doi.org/10.1007/s11854-013-0017-y