- #1
ryanj123
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Homework Statement
Allow D to be the circle lz+1l=1, counterclockwise. For all positive n, compute the contour integral.
Homework Equations
int (z-1/z+1)^n dz
The Attempt at a Solution
I know to use the extension of the CIF.
Where int f(z)/(z-zo)^n+1 dz = 2(pi)i* (f^(n)(zo)/n!) ...
However, I'm unsure how to execute the integral for my answer to depend on n.
I made f(z)=(z-1)^n
Then,
Int ( f(z)/(z+1)^n) = 2(pi)i*(f^n(zo)/n!)
Evaluating
f(zo) at zo=-1
= (-2)^n
So..
2(pi)i*((-2)^n/n!)
I know I'm missing components of the derivative operator... but I'm not sure how to go about completing this.
I appreciate any help.