private static Complex LogGamma_Stirling(Complex z)
{
// work in the upper complex plane; i think this isn't actually necessary
if (z.Im < 0.0)
{
return(LogGamma_Stirling(z.Conjugate).Conjugate);
}
Complex f = (z - 0.5) * ComplexMath.Log(z) - z + Math.Log(Global.TwoPI) / 2.0;
// reduce f.Im modulo 2*PI
// result is cyclic in f.Im modulo 2*PI, but if f.Im starts off too big, the corrections
// applied below will be lost because they are being added to a big number
f = new Complex(f.Re, AdvancedMath.Reduce(f.Im, 0.0));
Complex zz = z * z;
Complex zp = z;
for (int i = 1; i < AdvancedIntegerMath.Bernoulli.Length; i++)
{
Complex f_old = f;
f += AdvancedIntegerMath.Bernoulli[i] / (2 * i) / (2 * i - 1) / zp;
if (f == f_old)
{
return(f);
}
zp *= zz;
}
throw new NonconvergenceException();
}