Beta Function Calculator

Calculate beta function B(a,b), incomplete beta, and regularized incomplete beta functions.

Function Parameters

Beta Function Definition

B(a,b) = ∫₀¹ t^(a-1)(1-t)^(b-1) dt

= Γ(a)Γ(b)/Γ(a+b)

Quick Parameters

Beta Function B(2, 3)

0.08333333

Log Beta

-2.484907

I_x(2,3)

0.562500

Gamma Components

Γ(2)

1.0000

Γ(3)

2.0000

Γ(5)

24.0000

Beta Values Table

B(1, 1)1.000000
B(1, 2)0.500000
B(1, 3)0.333333
B(1, 4)0.250000
B(1, 5)0.200000
B(2, 2)0.166667
B(2, 3)0.083333
B(2, 4)0.050000
B(2, 5)0.033333
B(3, 3)0.033333

Properties

  • • B(a,b) = B(b,a) (symmetric)
  • • B(1,1) = 1
  • • B(a,b) = Γ(a)Γ(b)/Γ(a+b)
  • • Used in Beta distribution