This preview shows page 1. Sign up to view the full content.
Unformatted text preview: f ( z ) centered at z = 0 converges to f ( z ) for every z in C . (b) Let be a simple closed positively oriented contour. Suppose that f ( z ) is analytic everywhere on and inside except at a single point z 1 inside . If z 1 is a pole of order 2, then Z f ( z ) d z 6 = 0 . Problem 5. (10) Find the Laurent expansion of the function f ( z ) = 1 / ( z + z 2 ) that is valid in the annulus < | z + 1 | < 1. Problem 6. (10) Evaluate I | z | =1 e z ( z-2 i )( z-3) d z. Problem 7. (10) Evaluate I | z | =3 e z z ( z-2) 2 d z. 1...
View Full Document
This note was uploaded on 10/03/2011 for the course MATH 3364 taught by Professor Staff during the Spring '08 term at University of Houston.
- Spring '08
- Power Series