Math

Gamma Function Calculator

Evaluate the gamma function Γ(x), the continuous extension of factorial.

Calculated Output

Γ(x) 24

Formula: Γ(x) = (x − 1)! for positive integers; Lanczos approximation otherwise

Step-by-Step Breakdown

1. Values used:

2. x = 5

4. Γ(x) = 24

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The math behind it

For a positive integer n, Γ(n) = (n − 1)!. For other values it is computed with the Lanczos approximation, a fast and accurate series.

Γ(5) = 4! = 24.

What is Γ(½)?

Γ(½) = √π ≈ 1.7725.