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We want to calculate the following integral over the complex unit sphere $S^{2n-1}$: $$\int_{S^{2n-1}} \frac{1 }{|1 - \langle z, \zeta \rangle|^2} \, d\sigma(\zeta),$$ where $ z $ is a fixed point in ...

This is a simple question I asked in math.SE last month but unfortunately no one gives any comment. So I decided to try some luck here. You can skip examples below and read from "General setting" at ...