Gamma Function Calculator

About Gamma Function Calculator

The gamma function extends factorials to real numbers: Γ(n) = (n-1)! for positive integers. Γ(1/2) = √π.

How to use this calculator

1. Enter the value of \(n\) in the input box.
2. Check whether the input is a positive whole number, because the simple factorial-style rule applies there.
3. Read the displayed value of \(\Gamma(n)\).
4. Use the worked example to see how the calculator connects \(\Gamma(n)\) to factorial notation.

The formula explained

For positive whole numbers, the gamma function is given by \(\Gamma(n) = (n-1)!\). This means you subtract 1 from the input, then take the factorial of that result.

• n = the input value you want to evaluate
• \(\Gamma(n)\) = the gamma function value for the input
• ! = factorial, the product of all positive whole numbers up to that number

Step by step method

1. Start with the input \(n\).
2. Subtract 1 to get \(n-1\).
3. Compute the factorial \( (n-1)! \).

Worked example

Problem. Find \(\Gamma(6)\).

1. Use the rule \(\Gamma(n) = (n-1)!\), so \(\Gamma(6) = 5!\).
2. Calculate \(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\).
3. So \(\Gamma(6) = 120\).

Tips and common mistakes

• Remember that \(\Gamma(n)\) uses \(n-1\), not \(n\), before taking the factorial.
• The simple factorial rule works for positive whole numbers, so be careful with non-integers or negative inputs.

Frequently asked questions