Math

Gamma Function Calculator (Γ(x))

Enter a positive number.

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Γ(x)
Γ(x)
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ln Γ(x)
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Equivalent factorial
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Gamma Function Calculator (Γ(x)) by TheCalcTools

How the Gamma Function Calculator (Γ(x)) works

The gamma function extends the factorial to real numbers: Γ(n) = (n − 1)! for whole numbers, and Γ(x + 1) = x Γ(x). Γ(1/2) = √π.

The calculator uses the Lanczos approximation for ln Γ, accurate to about 15 significant digits, and exponentiates it.

The formula

Γ(x) = ∫₀^∞ t^(x−1) e^(−t) dt; Γ(n) = (n − 1)!

Worked example

Using the default values shown in the calculator:

x5.5
  1. Γ(5.5) = 52.342778, so 4.5! ≈ 52.3428.

Result:

Γ(x)52.3428
ln Γ(x)3.9578
Equivalent factorial4.5! = Γ(5.5)

Frequently asked questions

What is 4.5 factorial?

Γ(5.5) ≈ 52.3428.

Sources and further reading

Factorial CalculatorCalculate the factorial n! of a whole number Permutation and Combination CalculatorCount how many ways you can choose r items from n, with order (permutations) or without… Scientific CalculatorType an expression or tap the keys Binomial Distribution CalculatorCalculate binomial probabilities for n trials with success probability p

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