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On the growth of a meromorphic function and its derivatives. (English) Zbl 0643.30021

The relative rates of growth of a function F meromorphic in the complex plane and its qth derivative F (q) are studied via the Nevanlinna characteristics T(r,F) and T(r,F (q) ). It is shown that

lim infT(r,F)/T(r,F (q) )3e

for all meromorphic functions. A lower bound on the size of the set {r>1: T(r,F)/T(r,F (q) )3eK} for K>1 is obtained. The upper bounds established for T(r,F)/T(r,F ' ) justify in a weakened form an old conjecture of Nevanlinna.

Reviewer: W.K.Hayman

MSC:
30D35Distribution of values (one complex variable); Nevanlinna theory