Recent content by Cmeteorolite

  1. C

    How to deal with f(z) that is only analytic outside the unit disk?

    Thanks for your example~ Things are getting complicated if no explicit expression of f(z) is given. Is there a way of showing \int_{|w|=1}\frac{f(w)dw}{w^{n+1}}=0 for n=0,1,2,... ? Or it is a false statement ? Also for the |z|>1 part, can I just specify a circle with radius R>|z|, and...
  2. C

    How to deal with f(z) that is only analytic outside the unit disk?

    I guess the main difference between our wording is that we have exactly the opposite range of |z| ? I think the problem I wrote was correct since f(z) is only analytic outside the unit circle. So it seems to have exactly the opposite answer as what we originally expected. The normal case we...
  3. C

    How to deal with f(z) that is only analytic outside the unit disk?

    Homework Statement f(z) is analytic for |z|≥1. Let C be the unit circle. Show that the integral \frac{1}{2i\pi}\int_C\frac{f(w)}{wz-z^2}dw is 0 if |z|<1, is \frac{f(z)}{z} if |z|>1 Homework Equations The Attempt at a Solution For |z|<1 case, I tried to write the integral as \frac{1}{z2\pi...