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Complex Analysis: Cauchy Integral Formula

  1. Apr 29, 2010 #1
    1. The problem statement, all variables and given/known data
    The problem, for reference, is from Sarason's book "Complex Function Theory, 2nd edition" and is on page 81, Exercise VII.5.1.

    Let C be a counterclockwise oriented circle, and let f be a holomorphic function defined in an open set containing C and its interior. What is the value of the Cauchy Integral, [tex]\int_{C} \frac{f(\zeta)}{\zeta-z} d\zeta
    [/tex], when z is in the exterior of C?

    2. Relevant equations
    The Cauchy Integral formula, as mentioned in the problem.

    3. The attempt at a solution
    I haven't the slightest how to begin the problem. My intuition, though, tells me [tex]\int_{C} \frac{f(\zeta)}{\zeta-z} d\zeta=0[/tex]. Any insight is appreciated.
  2. jcsd
  3. Apr 29, 2010 #2


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    If z is in the exterior of C then f(zeta)/(zeta-z) is holomorphic in zeta over all of C.
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