超球の体積
n=2kの場合、
V 2 k ( R ) {\displaystyle V_{2k}(R)} = π k k ! R 2 k {\displaystyle ={\frac {\pi ^{k}}{k!}}R^{2k}} = ( 2 π ) k ( 2 k ) ! ! R 2 k {\displaystyle ={\frac {(2\pi )^{k}}{(2k)!!}}R^{2k}} = π k 1 ⋅ 2 ⋅ ⋯ ( k − 1 ) ⋅ k R 2 k {\displaystyle ={\pi ^{k} \over 1\cdot 2\cdot \cdots (k-1)\cdot k}R^{2k}}