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## Ball volume

### Definition

$ p\in \mathbb N $ |

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

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

### Discussion

#### Theorems

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

$V_p(r)= \pi^{p/2}\ \Gamma(p/2+1)^{-1}\ r^p $ |
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#### Reference

Wikipedia: Volume of an n-ball