Unformatted text preview: (15 pts) Let f be a non-constant entire function such that f ( n ) = 1998 for every n ∈ Z . Can f have at ∞ : a) an essential singularity, b) a pole, c) a removable singularity? 6. (15 pts) Suppose that f is analytic on D 1 (0) and that | f ( z ) | < 1 for all z ∈ D 1 (0). Prove that if f (0) = a 6 = 0, then f has no zeroes in the disk D | a | (0). 7. (15 pts) Show that a one-to-one entire function must be of the form az + b for some complex constants a and b with a 6 = 0....
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This document was uploaded on 01/25/2012.
- Spring '09