Unformatted text preview: f ( z ) centered at z = 0 converges to f ( z ) for every z in C . (b) Let Γ be a simple closed positively oriented contour. Suppose that f ( z ) is analytic everywhere on and inside Γ except at a single point z 1 inside Γ. If z 1 is a pole of order 2, then Z Γ 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 ( z2 i )( z3) d z. Problem 7. (10) Evaluate I  z  =3 e z z ( z2) 2 d z. 1...
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 Spring '08
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 Power Series, Taylor Series, γ, 1 g

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