Answer: B(m,n) = Gamma(m)Gamma(n)/Gamma(m+n).
- A B(m,n) = Gamma(m+n)/[Gamma(m)Gamma(n)]
- B B(m,n) = Gamma(m)Gamma(n)/Gamma(m+n)
- C B(m,n) = Gamma(m) + Gamma(n)
- D B(m,n) = m! × n!/(m+n)!
Correct answer: B. B(m,n) = Gamma(m)Gamma(n)/Gamma(m+n)
Explanation: Using the Gamma convolution: Γ(m)Γ(n) = ∫₀^∞ um−1e−udu · ∫₀^∞ vn−1e−vdv. Substituting u=t·s, v=t(1−s) and integrating out t gives B(m,n) = Γ(m)Γ(n)/Γ(m+n).
The exact area under the curve from a to b (shaded) is approximated by a few rectangles, the Riemann sum idea behind the definite integral.