Β関数

Β関数について次の公式が成り立つ．

$$B\left(x,y\right)=2 \int_0^{\frac{\pi}{2}} \sin^{2x-1}\theta\cos^{2y-1}\theta d\theta$$ $$B\left(x,y\right)= \frac{\Gamma\left( x\right)\Gamma\left( y\right)}{\Gamma\left( x+y\right)}$$