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Hi,

I was wondering whether there was an explicit formula for the following integral:

$$\int_{B_r}\int_{B_r}|x-y|^{-(d-1)} dx dy$$

Here $dx$ and $dy$ is lebesgue measure on $R^d$ and $B_r$ is some ball of radius $r$.

I was able to write down an expression for it using polar coordinates and areas of spherical caps but the thing is nasty.

It seems rather strange that I have never seen a solution to this.

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Why is that strange? Why do you feel that you should have seen a computation of this integral? Where does it arise? Unless you provide some background and motivation for this problem, it will likely be closed for being too localized/not research level. –  MTS Apr 16 '12 at 5:06
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closed as too localized by plusepsilon.de, MTS, Anthony Quas, Yemon Choi, Zev Chonoles Apr 16 '12 at 6:03

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