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This is a weird problem that I could use some hints on how to solve:

If $f:\mathbb{C}\to \mathbb{C}$ is analytic and for some $k \in \mathbb{N}$ there exist constants $C_1,C_2>0$ such that $$|f(z)|\leq C_1 + C_2|z|^k$$ then $f$ is a polynomial of degree at most $k$.

I am pretty much stumped here. Can you guide me/provide some hints?

Numbersandsoon
  • 2,910
  • http://math.stackexchange.com/questions/86772/show-that-if-fz-leq-m-zn-then-f-is-a-polynomial-max-degree-n?rq=1 – Myshkin Oct 15 '13 at 03:02
  • http://math.stackexchange.com/questions/438310/show-that-an-entire-function-is-a-polynomial?rq=1 – Myshkin Oct 15 '13 at 03:05

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