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Let $f$ be an entire function such that $|f(z)|\leq A+B|z|^k$ for all $z$, where $A$, $B$, $k$ are positive numbers.

Prove that $f$ is polynomial.

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    By "full" I'm guessing you mean ["entire"](http://en.wikipedia.org/wiki/Entire_function). Please consider adding some remarks on what you've tried for this problem.2012-07-02
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    Hint: show that the n'th derivatives of $f$ begin to vanish at a certain point, using Cauchy's theorem2012-07-02

3 Answers 3