Which of the following is the correct definition of the Beta function B(α,β)B(\alpha, \beta)B(α,β)?
∫01xα−1(1−x)β−1dx\int_0^1 x^{\alpha-1} (1-x)^{\beta-1} dx∫01xα−1(1−x)β−1dx
∫0∞xα−1e−xdx\int_0^\infty x^{\alpha-1} e^{-x} dx∫0∞xα−1e−xdx
Γ(α)Γ(β)Γ(α+β)\frac{\Gamma(\alpha)\Gamma(\beta)}{\Gamma(\alpha+\beta)}Γ(α+β)Γ(α)Γ(β)
Both a and c.