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Q46Section II (Mathematics)46 of 190

A strict derivative bound forces exponential form, and hence f"=cf′f"=cf'

Let f:C→Cf:\mathbf C\to\mathbf C be a non-constant analytic such that ∣f′(z)∣<∣f(z)∣|f'(z)|<|f(z)| for all z∈Cz\in\mathbf C. Then:

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