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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
Picard value
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