Ball volume

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$ p\in \mathbb N $

$V_p:\mathbb R_+\to \mathbb R_+$

$V_p(r):=\beta^p(B_0(r))$

For all $a\in \mathbb R^p$, the volume of the ball $B_a(r)$ is the same and given by

$V_p(r)=\frac{\pi^{p/2}}{\Gamma(p/2+1)} r^p$