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Complex analysis formula for an integral

  1. Sep 28, 2011 #1
    1. The problem statement, all variables and given/known data

    Find a formula for:

    [itex]\int[/itex][itex]1/(z-a)m(z-b)n[/itex]dz

    around a ball of radius R, centred at z0

    where |a| < R < |b| and m,n[itex]\in[/itex]N.


    2. Relevant equations

    Not sure which equations to use, a cauchy integral formula maybe...?

    3. The attempt at a solution

    I've attempted to split the fraction up into partial fractions, so that the integral is now:

    [itex]\int[/itex][itex]1/(z-a)m(b-a)n[/itex]+[itex]1/(z-b)n(b-a)m[/itex]dz

    but I don't think this has made it any easier to solve...

    any suggestions?
     
  2. jcsd
  3. Sep 28, 2011 #2

    lanedance

    User Avatar
    Homework Helper

    so do you mean
    [tex] \int \frac{1}{(z-a)^m(z-b)^n} dz[/tex]

    how about considering poles & residues?
     
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