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Unformatted text preview: the class for cot z ), and apply the Residue theorem with it to the function f ( z ) cot πzdz . Using the fact that  f ( z )  ≤ 1 n 2a 2 to show that lim n → + ∞ Z γ n f ( z ) cot πzdz = 0 . 3. Page 149, #30, #32 on the textbook 4. Determine which of the following family is normal. (a) F = { z n } ∞ n =1 on the unitdisc D (0 , 1). (b) F = { z n 1 / 2 } ∞ n =1 on the whole complex plane C . (c) F = { f ( z ) ≡ c for some c ∈ C } on whole complex plane C . 6. Let U ⊂ C be a connected open set. Show that the family F = { f  f is holomorphic on U and Re ( f ) > } is normal. 1...
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This note was uploaded on 02/21/2012 for the course MATH 4377 taught by Professor Staff during the Summer '08 term at University of Houston.
 Summer '08
 Staff
 Math

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