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On the behaviour of the successive derivatives of meromorphic functions on the final set

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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Correspondence to Thierry Meyrath.

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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

Keywords

  • Natural Number
  • Entire Function
  • Meromorphic Function
  • Principal Part
  • Successive Derivative