Gamma Function Calculator
Calculate gamma function Γ(z), log-gamma, digamma, and trigamma functions.
Function Parameters
Gamma Function Definition
Γ(z) = ∫₀^∞ t^(z-1) e^(-t) dt
For positive integers: Γ(n) = (n-1)!
Quick Values
Special Values
Γ(1/2) = √π1.772454
Γ(1) = 11.000000
Γ(3/2) = √π/20.886227
Γ(2) = 11.000000
Γ(5/2) = 3√π/41.329340
Gamma Function Γ(5)
2.40000000e+1
= (4)!
Log Gamma ln(Γ)
3.178054
Digamma ψ(z)
1.506118
Trigamma ψ'(z)
0.225160
Gamma for Integers
Γ(1) = 0!1
Γ(2) = 1!1
Γ(3) = 2!2
Γ(4) = 3!6
Γ(5) = 4!24
Γ(6) = 5!120
Γ(7) = 6!720
Γ(8) = 7!5040
Γ(9) = 8!40320
Γ(10) = 9!362880
Properties
- • Γ(z+1) = z·Γ(z)
- • Γ(n) = (n-1)! for integers
- • Γ(1/2) = √π
- • ψ(z) = d/dz ln(Γ(z))