Dave's Math Tables: Beta Function
(Math | Calculus | Integrals | Special Functions | Beta Function)

B(x,y) = (integral)(0 to 1) t^(x-1) (1-t)^(y-1) dt

 B(x,y) = 2 (integral)(0 to PI/2) (sin t)^(2x-1) (cos t)^(2y-1) dt
B(x,y) = (integral)(0 to inf) t^(x-1) / (1+t)^(x+y) dt

 B(x,y) = B(y,x)
B(x,y) = gamma(x)gamma(y) / gamma(x+y) (gamma(x) = Gamma Function)

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