The Liouville theorem state:
Let $f$ be an entire function for which there exists a positive number M such that $|f(z)|\leq M$ for all z in $\mathbb{C}$, the $f$ must be a constant.
more general form of this theorem is :
Let $f$ be an entire function for which there exists a positive number M and a polynomial $P$ such that $|f(z)|\leq M |P(z)|$ for all z in $\mathbb{C}$ then $f(z)=k P(z)$ for $k$ a constant.
who know a good proof of this generalized form ?