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
HAYMAN, W.K.: Meromorphic functions. Oxford: Clarendon Press 1975
NEVANLINNA, R.: Le théorème de Picard-Borel et la théorie des fonctions méromorphes. Paris: Gauthier-Villars 1929
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
WITTICH, H.: Neuere Untersuchungen über eindeutige analytische Funktionen. Berlin-Göttingen-Heidelberg: Springer 1968
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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