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Topic: entire function and polynoials (Read 8303 times) 

MonicaMath
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entire function and polynoials
« on: Feb 26^{th}, 2009, 11:56am » 
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Hi everybody... I have a BIG problem that needs to solve: if f(z) is an entire function with f(z)<=Bz^S, for all z in C, (1) Should S be an integer and why, (2) can we write f as: f(z)=A z^j, for some A in C, with A<=B. please can one help me in soving this problem.


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Eigenray
wu::riddles Moderator Uberpuzzler
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Re: entire function and polynoials
« Reply #1 on: Feb 26^{th}, 2009, 7:56pm » 
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The conclusion should be that f(z) is a polynomial of degree no more than S. Are you familiar with Liouville's theorem? Try to generalize the proof there to show that a_{k} = 0 for k > S.


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