I am facing trouble in evaluating some double integral. The definition of Riesz energy is given by $I_t(U)=\int_U\int_U|x-y|^{-t}\ dx\ dy$ where $U$ is an open subset. For better understanding I want to calculate this integral in ball i.e say $\int_{B(s,r)}\int_{B(s,r)}|x-y|^{-t}\ dx\ dy$. I know how to do $\int_{B(x,r)}|x|^{-t}$ using polar coordinates change. But here it's double integral, can anyone let me know how to calculate this integral for balls?
2026-03-28 00:46:40.1774658800
Finding double integral over balls
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