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Unformatted text preview: has an analytic antiderivative on C { } . 4. Find all real valued harmonic functions on the plane that are constant on all vertical lines. 5. It is a fact that, if n Z , then 1 sin 2 z1 ( zn ) 2 has a removable singularity at z = n . a) Demonstrate this fact in case n = 0. b) Prove that X n = 1 ( zn ) 2 converges uniformly on every bounded set after dropping nitely many terms. c) Finally, use Liouvilles Theorem to prove that 1 sin 2 z = X n = 1 ( zn ) 2 ....
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This document was uploaded on 01/25/2012.
 Spring '09
 Math

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