I am intersted in Example of entire function on $\mathbb C$ such that which does not take only one value in $\mathbb C$ .
I know that it is not possible for entire function to leave only some open ball in $\mathbb C$ .
I know how to prove that .
Is there exist such example?
Any help will be appreciated
2026-03-25 12:23:56.1774441436
Example of entire function on $\mathbb C$ such that which does not take only one value in $\mathbb C$
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Sure. If $a\in\mathbb C$, take $f(z)=e^z+a$. Then the range of $f$ is $\mathbb{C}\setminus\{a\}$ and $f$ is entire.