The function B(p,q)=∫01xp−1(1−x)q−1dx=Γ(p)Γ(q)Γ(p+q) where Γ(a) is the gamma function. For positive integers m, n, B(m,n)=(n−1)!(m−1)!(m+n−1)!.
The beta function B is given bywhere a>0, b>0. The function is symmetric, i.e. B(a, b)=B(b, a), for all a, b.
The beta function is related to the gamma function Γ byIf a and b are positive integers then
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