find all possible entire functions f with the property that $|f(z)|\le2|z|+1$ for all $z\in C$. Prove that you have found all such functions.
First of all I am self studying complex analysis so sorry if i am not very precise on thrms or...
My idea is : since f is entire, then it is analytic in all complex plane.
can I say f is bounded in complex plane? then by liouville's thm or maximum modulus principle claim that f can only be a constant function?
if yes, how should I prove my claim. and how should I prove I have found ALL possible functions f?
2025-01-13 05:42:36.1736746956
prove you have found all such functions
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