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Picardsche Ausnahmewerte von Ableitungen gewisser meromorpher Funktionen. (German) Zbl 0537.30017
It is an easy consequence of the second fundamental theorem of Nevanlinna that each derivative \(g^{(n)}\), \(n\in {\mathbb{N}}\), of a transcendental meromorphic function g has at most one finite Picard value. Generalizing a result of Mues we prove that for \(g=f^{n+2}\) only zero can be this Picard value. The functions \(f=R \exp P,\) R rational, P polynomial, show that Picard value zero can actually occur. We show that for \(k\geq n\), \(n\geq 3\), \((f^ k)^{(n)}\) has Picard value zero only if f is of this form.

MSC:
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
Keywords:
Picard value
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