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Cmeteorolite
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Homework Statement
f(z) is analytic for |z|≥1. Let C be the unit circle. Show that the integral [itex]\frac{1}{2i\pi}\int_C\frac{f(w)}{wz-z^2}dw[/itex] is 0 if [itex]|z|<1[/itex], is [itex]\frac{f(z)}{z}[/itex] if [itex]|z|>1[/itex]
Homework Equations
The Attempt at a Solution
For [itex]|z|<1[/itex] case, I tried to write the integral as
[itex]\frac{1}{z2\pi i}\int_C\frac{f(w)}{w-z}dw[/itex] and write the integrand as a series
[itex] \frac{f(w)}{w}\sum_{n=0}^\infty(\frac{z}{w})^n [/itex] which converges uniformly, then interchange integral with summation ... I tried to show that every term under the summation is 0 but didn't make it...