public class GammaFunction {

	public double st_gamma(double x){
		return Math.sqrt(2*Math.PI/x)*Math.pow((x/Math.E), x);
	}
	
	public double la_gamma(double x){
		double[] p = {0.99999999999980993, 676.5203681218851, -1259.1392167224028,
			     	  771.32342877765313, -176.61502916214059, 12.507343278686905,
			     	  -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7};
		int g = 7;
		if(x < 0.5) return Math.PI / (Math.sin(Math.PI * x)*la_gamma(1-x));

		x -= 1;
		double a = p[0];
		double t = x+g+0.5;
		for(int i = 1; i < p.length; i++){
			a += p[i]/(x+i);
		}
		
		return Math.sqrt(2*Math.PI)*Math.pow(t, x+0.5)*Math.exp(-t)*a;
	}
	
	public static void main(String[] args) {
		GammaFunction test = new GammaFunction();
		System.out.println("Gamma \t\tStirling \t\tLanczos");
		for(double i = 1; i <= 20; i += 1){
			System.out.println("" + i/10.0 + "\t\t" + test.st_gamma(i/10.0) + "\t" + test.la_gamma(i/10.0));
		}
	}
}