// by Tim Ratigan
// Plots the phase for the reciprocal of the gamma function

public class PhaseInvGamma implements ComplexFunction {
    public Complex eval(Complex z) { // \arg\frac{1}{\Gamma(z)}
        double gamma = .5772156649;
        Complex one = new Complex(1.0, 0);
        Complex fact = z.times(z.times(gamma).exp());
        for (int i = 1; i < 10; i++) {
            fact = fact.times(one.plus(z.times(1.0/i)));
            fact = fact.times(z.times(-1.0/i).exp());
        }
        
        return new Complex(fact.phase(), 0);
    }

    public static void main(String[] args) {
        Plot2Dez.show(new PhaseInvGamma(), 512);
    }
}