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Formulas: formula-gamma: $B(a,b)=\Gamma(a)\Gamma(b)/\Gamma(a+b)$.- formula-integral: For $a>0$ and $b>0$, $B(a,b)=\int_0^1 t^{a-1}(1-t)^{b-1}\,dt$.- formula-trigonometric: For $a>0$ and $b>0$, $\int_0^{\pi/2}\sin^{2a-1}(\theta)\cos^{2b-1}(\theta)\,d\theta+ formula-integral: For $a>0$ and $b>0$, $B(a,b)=\int_0^1 t^{a-1}(1-t)^{b-1}\,\mathrm{d}t$.+ formula-trigonometric: For $a>0$ and $b>0$, $\int_0^{\pi/2}\sin^{2a-1}(\theta)\cos^{2b-1}(\theta)\,\mathrm{d}\theta =B(a,b)/2$. formula-reflection: For $0<a<1$, $B(a,1-a)=\pi/\sin(\pi a)$.
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