Gamma Function Calculator

Calculate the Gamma function Γ(x)

x value (avoid non-positive integers)

Definition

Γ(x) = ∫₀^∞ t^(x-1) e^(-t) dt

Euler's integral

Factorial Extension

Γ(n) = (n-1)!

For positive integers n

Recurrence

Γ(x+1) = x·Γ(x)

Fundamental property

Reflection Formula

Γ(x)·Γ(1-x) = π/sin(πx)

Euler's reflection formula

Statistics

• Probability distributions

• Beta function

• Chi-squared distribution

Physics

• Quantum mechanics

• Statistical mechanics

• Special functions

Mathematics

• Complex analysis

• Number theory

• Integral calculus

Γ(1) = 1

Γ(2) = 1

Γ(1/2) = √π ≈ 1.7724

Γ(3) = 2

Γ(4) = 6

Γ(5) = 24