B. ガウスの積分公式

$$\int_0^{\infty} x^{2n} \exp\left(-\lambda x^2\right)dx = \frac{\left(2n-1\right)!!}{2^{n+1}} \sqrt{\frac{\pi}{\lambda^{2n+1}}} , \quad n\in {\bf N}$$ (23)