Work out gamma function instantly with clear inputs, formula shown and shareable results.
The gamma function extends the factorial to non-integers, with Γ(n) = (n − 1)! for positive integers. It satisfies the recurrence Γ(z + 1) = z·Γ(z) and has poles at zero and the negative integers. This uses the Lanczos approximation.
Gamma recurrence
Γ(z + 1) = z·Γ(z), Γ(n) = (n − 1)! for whole n
Reflection
Γ(z)·Γ(1 − z) = π / sin(πz)
√π ≈ 1.7724539, one of the most quoted values of the function.
The recurrence forces Γ(z) to blow up as z approaches 0, and stepping down by the recurrence propagates that to every negative integer.