There is a theorem [Liouville's theorem...] that states that every bounded entire function is a constant. A function f(*) is said to be 'bounded' if exists a positive number M such that for all z in C is |f(z)| < M...
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If f is an entire function how does one show that f is a non-constant polynomial iff. lim z-> infinity |f(z)| = infinity?
the questions suggests that I look at how the MacLaurin series for f and the Laurent series for g(z) =f(1/z) are related and what kind of singularity g has at 0 but i'm not quite sure where to go with that...