This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: z ) g ( z ) is real for all z D . Prove that f = cg where c is a real constant, or g . 6. Let f be an analytic function in the region { z : 0 <  z  < 1 } , and suppose that it satises  f ( z )  A + B  z  for some positive numbers A,B and . Prove that f is meromorphic in the unit disc (that is 0 is either a pole or a removable singularity of f ). 7. Let f = X n =1 a n z n be a conformal map from the unit disc onto the square { z : < z  < 1 , = z  < 1 } . Prove that a n = 0 for all n 6 = 4 k + 1 , k = 0 , 1 , 2 , 1 .... 1 8. Evaluate the integral Z log x 1 + x 2 . Hint: integrate log z/ (1 + z 2 ) over the boundary of the region { z : <  z  < R, = z > } . 2...
View
Full
Document
This document was uploaded on 01/25/2012.
 Spring '09
 Math

Click to edit the document details