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${f_n(z)}$ be a sequence of analytic function in a domain $D$ such that $f_n\to f$ uniformly in $D$. Then $f_n’\to f'$ uniformly in $D$.

How can I show that the above statement is true/false?

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    Hint: Cauchy's formula gives a representation of derivatives that plays nicely with uniform convergence.2012-11-23
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    You need to show more. You first need to show that $f$ is differentiable, otherwise the conclusion doesn't necessarily make sense.2012-11-23

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