The Beta function is symmetric, meaning <math>B(x,y) = B(y,x)</math>.
It has many other forms, including:
&=& 2\int_0^\frac{\pi}{2}\sin^{2x1}\theta\cos^{2y1}\theta\,d\theta, & {\mathcal Re}(x)>0, {\mathcal Re}(y)>0\\&=&\int_0^\infty\frac{t^{x1}}{(1+t)^{x+y}}\,dt, & {\mathcal Re}(x)>0, {\mathcal Re}(y)>0 \\ &=&\frac{1}{y}\sum_{n=0}^\infty(1)^n\frac{(x)_{n+1}}{n!(x+n)}, \end{matrix}</math>
where <math>(x)_{n}</math> is the falling factorial.
See also: Euler integral, falling factorial, Gamma function
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