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October 16th, 2012, 10:19 PM   #1
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Find all entire functions f

Find all the entire functions f such that
and
for all .


My attempt at this question...
Let .
Since and are entire and (since ).
is entire & .
By Liouville's Theorem, for some .
for some , since .
Hence
Now it is given that , and , hence .


Is this correct? Are there any other solutions? Any improvement/suggestion is welcomed! Thanks in advance!.
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October 17th, 2012, 12:49 AM   #2
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Re: Find all entire functions f

Sorry, for the question it should be instead of
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