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How would one show that if $\displaystyle \lim_{z \to 0} z \exp(f(z))$ exists, where $f: \mathbb{C}^\ast \longrightarrow \mathbb{C}$ is holomorphic, then it must be zero? Is this even true?

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    It means that $\exp(f(z))$ cannot have a simple pole.2012-05-21

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