/// <summary>
/// Calculates the specified Gamma function when <paramref name="a"/> is a half integer
/// </summary>
/// <param name="r"></param>
/// <param name="a"></param>
/// <param name="x"></param>
/// <returns></returns>
static double HalfIntegerA(Routine r, double a, double x)
{
Debug.Assert(a - Math.Floor(a) == 0.5);
double sum = 0;
if (a > 1)
{
sum = 1.0;
double term = 1.0;
for (int n = 2; n < a; ++n)
{
term *= x / (n - 0.5);
sum += term;
}
}
double result;
double mult = 2.0 * Constants.RecipSqrtPI * Math.Sqrt(x);
if (r == Routine.Q || r == Routine.Upper)
{
result = Math2.Erfc(Math.Sqrt(x)) + sum * mult * Math.Exp(-x);
return((r == Routine.Q) ? result : result *Math2.Tgamma(a));
}
else
{
result = Math2.Erf(Math.Sqrt(x)) - sum * mult * Math.Exp(-x);
return((r == Routine.P) ? result : result *Math2.Tgamma(a));
}
}
/// <summary>
/// Asymptotic expansions of the incomplete gamma function P(a, x),
/// used when a is large and x ~= a.
/// </summary>
/// <param name="a"></param>
/// <param name="x"></param>
/// <returns></returns>
public static double GammaP(double a, double x)
{
double sigma = (x - a) / a;
double phi = -Math2.Log1pmx(sigma);
double y = a * phi;
double z = Math.Sqrt(2 * phi);
if (x < a)
{
z = -z;
}
double p = Polynomial.Eval(_C, z, 1 / a);
double result = p * (Math.Exp(-y) * (Constants.RecipSqrt2PI / Math.Sqrt(a)));
if (x < a)
{
result = -result;
}
result += Math2.Erfc(Math.Sqrt(y)) / 2;
return(result);
}