Beta function
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https://en.wikipedia.org/wiki/Beta_function
\(\displaystyle \mathrm {B} (x,y)=\int _{0}^{1}t^{x-1}(1-t)^{y-1}\,dt\)
for Re \(x\), Re \(y > 0\).
\(\displaystyle \mathrm {B} (x,y)=\mathrm {B} (y,x) = \frac{\Gamma (x)\,\Gamma (y)}{\Gamma (x+y)} ={\dfrac {(x-1)!\,(y-1)!}{(x+y-1)!}} \)