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# Liouville and Cauchy Estimates watch

1. Code:
Let f be an entire function. Suppose that

for all z with |z|  1. Prove that f is a polynomial of degree at
most 3. Also prove that  where each 
Proving that f is a polynomial of degree at most 3 is easy but I can't seem to get the required constraint for . In examples we've seen the bound on f has been for all z and f(0), f'(0) etc have been used to single out each co-efficient but I can't seem to single them out easily with this bound for |z| 1.

Any clues?

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Updated: March 25, 2013
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