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Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen

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Abstract

In this paper it is shown that the functions f(z)=αez are the only nonconstant entire (meromorphic) functions which share two (three) distinct finite values with their derivative.

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Literatur

  1. HAYMAN, W.K.: Meromorphic functions. Oxford: Clarendon Press 1975

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  2. NEVANLINNA, R.: Le théorème de Picard-Borel et la théorie des fonctions méromorphes. Paris: Gauthier-Villars 1929

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  3. RUBEL, L.A., YANG, C.C.: Values shared by an entire function and its derivative. Complex Analysis (Proc. Conf. Univ. Kentucky, Lexington, Ky., 1976), 101–103. Lecture Notes in Mathematics, Vol. 599, Berlin: Springer 1977

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  4. WITTICH, H.: Neuere Untersuchungen über eindeutige analytische Funktionen. Berlin-Göttingen-Heidelberg: Springer 1968

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Authors and Affiliations

  1. Institut für Mathematik, Universität Hannover, Welfengarten 1, D-3000, Hannover 1

    Erwin Mues

  2. Mathematisches Institut I, Universität Karlsruhe, Englerstr. 2, D-7500, Karlsruhe 1

    Norbert Steinmetz

Authors
  1. Erwin Mues
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  2. Norbert Steinmetz
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Mues, E., Steinmetz, N. Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen. Manuscripta Math 29, 195–206 (1979). https://doi.org/10.1007/BF01303627

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  • DOI: https://doi.org/10.1007/BF01303627

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