# Integral on the circle

1. Sep 3, 2014

### Likemath2014

How I can show the following

$$\int _{\mathbb{T}} \frac{1}{|1-e^{-i\theta}z|^2}dm(e^{i\theta})= \frac{1}{1-|z|^2} ,$$
where z is in the unit disc
dm is the normalized Lebesgue measure and
T is the unite circle.

2. Sep 18, 2014

### Staff: Admin

I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?

3. Sep 22, 2014

### lavinia

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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