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Integral on the circle

  1. Sep 3, 2014 #1
    How I can show the following

    [tex] \int _{\mathbb{T}} \frac{1}{|1-e^{-i\theta}z|^2}dm(e^{i\theta})= \frac{1}{1-|z|^2} ,[/tex]
    where z is in the unit disc
    dm is the normalized Lebesgue measure and
    T is the unite circle.
     
  2. jcsd
  3. Sep 18, 2014 #2
    I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?
     
  4. Sep 22, 2014 #3

    lavinia

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    Gold Member

    This is a special case of the Poisson formula in the unit disc. Here the harmonic function is the constant function f(z) = 1.
     
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