Gamma Function

The Gamma Function is an important special function in mathematics. Its values can be expressed in closed form for integer and half-integer arguments, but no simple expressions are known for its values at rational points in general.

Assumptions

n is an integer, or half-integer, of any sign. For negative integers, Γ(n) = ∞.

Use

mctad.Γ(n) or mctad.gamma(n)

Inline Comments

mctad.Γ = function(n) { if (!mctad.isInteger(n * 2)) { return undefined; } if (n <= 0 && mctad.isInteger(n)) { return Infinity; } var Γ;

If n is a positive Integer, return its factorial, n!.

if (mctad.isInteger(n)) { Γ = mctad.factorial(n - 1); } else {

If (n / 2) is a positive Integer, return the exact value using double factorials, n!!.

if (mctad.isInteger(2 * n)) { Γ = (Math.sqrt(mctad.π) * mctad.doubleFactorial(n * 2 - 2) / Math.pow(2, (n * 2 - 1) / 2)); } } return Γ; }; mctad.gamma = mctad.Γ;