How to make a function that computes the factorial for numbers with decimals?

Question

How can I make a function that calculates the factorial (or the gamma function) of decimal numbers in JavaScript? For example, how could I calculate 2.33!?

Answer 1

I might have found an existing solution... It's an implementation of Lanczos method, I found it at the swedish wikipedia (http://sv.wikipedia.org/wiki/Gammafunktionen). It was written in python and says to be correct up to 15 decimals. I ported it to js, cross checked some random values against (http://www.efunda.com/math/gamma/findgamma.cfm).

http://jsfiddle.net/Fzy9C/

var g = 7;
var C = [0.99999999999980993, 676.5203681218851, -1259.1392167224028,771.32342877765313, -176.61502916214059, 12.507343278686905, -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7];

function gamma(z) {

    if (z < 0.5) return Math.PI / (Math.sin(Math.PI * z) * gamma(1 - z));
    else {
        z -= 1;

        var x = C[0];
        for (var i = 1; i < g + 2; i++)
        x += C[i] / (z + i);

        var t = z + g + 0.5;
        return Math.sqrt(2 * Math.PI) * Math.pow(t, (z + 0.5)) * Math.exp(-t) * x;
    }
}

(and ofcourse it does not support imaginary numbers, since js does not)