week2-hw - ∞ X n =2 z 2 n 1(2 n 1 ∞ X n =1 n n n z n 6...

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1. f = u + iv is holomorphic in D . Show that if u 2 + v 2 is constant, then f is constant. 2. (for grade) u = x 2 - y 2 + ax . Find all v such that f = u + iv is holomorphic for all z C . 3. (for grade) f ( z ) = e - 1 /z when z 6 = 0. Show that Cauchy-Riemann equa- tions are satisfied for all z C , z 6 = 0. 4. f = k =0 c k x k find all c k such that f is holomorphic. 5. (for grade) Find the radius of convergence of
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Unformatted text preview: ∞ X n =2 z 2 n +1 (2 n + 1)! , ∞ X n =1 n ! n n z n 6. Find the domain of convergence of ∞ X n =1 n ( z-i ) n 7. Let f be an entire function (analytical in C ) of the form f ( x,y ) = u ( x ) + iv ( y ). 8. (for grade) B.Ch. p.121, 3 9. B.Ch. 136, 8,9,10. 1...
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This note was uploaded on 05/03/2010 for the course MATH 185 taught by Professor Lim during the Summer '07 term at Berkeley.

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