What special properties do holomorphic and meromorphic complex functions $f(z)$ have if their derivative $f'(z_0) = 0$ is zero at some point $z_0$?
Complex functions with zero derivative at some point
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complex-analysis
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1It means that locally at $z_0$ the map $f$ is not conformal. – 2017-02-02
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0@Crostul, thank you for the reply. Is it the only property? Is it valid only for holomorphic functions? – 2017-02-02
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1It's better to say what property has missed when $f'(z_0)=0$ – 2017-02-02
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1$f$ has a neighbourhood where it is NOT injective. – 2017-02-06