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Unformatted text preview: b is the boundary ∂D (0 , 1) traversed once counterclockwise. 4. (a) Let the Laurent expansion of cot( πz ) on A (0;1 , 2) be cot( πz ) = ∞ X n =∞ a n z n . Compute a n for n < 0. (b) For n = 0 , 1 , 2 ,..., compute 1 2 πi Z Γ n dz z 3 sin z where Γ n is the circle ∂D (0 ,r n ) traversed once counterclockwise and r n = ( n + 1 2 ) π . Date : Posted: December 5, 2009. 1 5. (a) Does the following function have an antiderivative on A (0;4 , ∞ )? z ( z1)( z2)( z3) (b) Does the following function have an antiderivative on A (0;4 , ∞ )? z 2 ( z1)( z2)( z3) 2...
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 Fall '07
 Lim
 Math, Essential singularity

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