// series for L=0 for both F and G
// this has the same convergence properties as the L != 0 series for F above
private static void Coulomb_Zero_Series(double eta, double rho, out double F, out double FP, out double G, out double GP)
{
if (rho == 0.0)
{
double C = CoulombFactorZero(eta);
F = 0.0;
FP = C;
G = 1.0 / C;
GP = Double.NegativeInfinity;
return;
}
double eta_rho = eta * rho;
double rho_2 = rho * rho;
double u0 = 0.0;
double u1 = rho;
double u = u0 + u1;
double up = u1;
double v0 = 1.0;
double v1 = 0.0;
double v = v0 + v1;
for (int n = 2; n <= Global.SeriesMax; n++)
{
double u2 = (2.0 * eta_rho * u1 - rho_2 * u0) / (n * (n - 1));
double v2 = (2.0 * eta_rho * v1 - rho_2 * v0 - 2.0 * eta * (2 * n - 1) * u2) / (n * (n - 1));
double u_old = u;
u += u2;
up += n * u2;
double v_old = v;
v += v2;
if ((u == u_old) && (v == v_old))
{
double C = CoulombFactorZero(eta);
F = C * u;
FP = C * up / rho;
double r = AdvancedComplexMath.Psi(new Complex(1.0, eta)).Re + 2.0 * AdvancedMath.EulerGamma - 1.0;
G = (v + 2.0 * eta * u * (Math.Log(2.0 * rho) + r)) / C;
GP = (FP * G - 1.0) / F;
return;
}
u0 = u1; u1 = u2; v0 = v1; v1 = v2;
}
throw new NonconvergenceException();
}
