This preview shows page 1. Sign up to view the full content.
Unformatted text preview: at a . 3. Let C be a region. Let a and f : \{ a } C be a function with an isolated singularity at a . Suppose for some m N and > 0, Re f ( z ) m log  za  for all z D * ( a, ). Show that a is a removable singularity of f . 4. Let f : C C be analytic on C with a pole of order 1 at 0. Show that if f ( z ) R for all  z  = 1, then for some C and R , f ( z ) = z + 1 z + for all z C . 5. Let f : D * (0 , 1) C be analytic. Show that if  f ( z )  log 1  z  for all z D * (0 , 1), then f 0. Date : November 15, 2007 (Version 1.0); posted: November 15, 2007; due: November 21, 2007. 1...
View
Full
Document
This note was uploaded on 08/01/2008 for the course MATH 185 taught by Professor Lim during the Fall '07 term at University of California, Berkeley.
 Fall '07
 Lim
 Math

Click to edit the document details