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Unformatted text preview: 5. Let f ( z ) = a n z n ,g ( z ) = b n z n be analytic in U : { z  < 1 } and continuous on U , oriented counterclockwise. Prove that 1 2 i Z U f ( ) g ( z/ ) d = X a n b n z n ( z U ) (You must justify all steps in your argument.) 6. Let R be the boundary of the rectangle with vertices (3 , 2) , (+3 , 2), and let F ( z ) = Z R ze 2   2 d ( z ) 2 . (a) Prove that F is analytic inside R . (b) Try to obtain as good an upper bound for  F 00 (0)  as possible....
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This document was uploaded on 01/25/2012.
 Spring '09
 Math

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