Sterling’s approximation for the factorial function, even for small values of x. Out of my own interest, I wanted to know how accurate it is.

We can evaluate the accuracy for a few values of x. With the following script:

// The factorial way
var factorial = 1;
var curValue = input;
while (curValue > 0) {
factorial *= curValue;
curValue -= 1;
}

// The Sterling way
var approx = Math.pow(input, input) * Math.pow(Math.E, -input) * Math.sqrt(2 * Math.PI * input);


Factorial:
Approximation: