Beta integral
= Beta integral
{title2=$B(a,b)=\int_0^1x^{a-1}(1-x)^{b-1}\,dx$}
For positive <real numbers> $a,b$, the beta integral represents the <beta function> by $B(a,b)=\int_0^1x^{a-1}(1-x)^{b-1}\,dx$. In particular, for <nonnegative integers> $m,n$, it gives $\int_0^1x^m(1-x)^n\,dx=m!n!/(m+n+1)!$, connecting <integration> to <binomial coefficients>.