/// <summary>
/// Simple, stable, but not very accurate LogGammaP for small z < 0.7*a
/// <para>Log((z^a)(e^-z)/(a*Γ(a)) * 1F1(1, a+1, z))</para>
/// </summary>
/// <param name="a"></param>
/// <param name="z"></param>
/// <returns></returns>
static double LogGammaPSmallZ(double a, double z)
{
// See: http://dlmf.nist.gov/8.5#E1
double t = HypergeometricSeries.Sum1F1(1, a + 1, z, -1);
double result = a * Math.Log(z) - z - Math2.Lgamma(1 + a) + Math2.Log1p(t);
return(result);
}
/// <summary>
/// Lower gamma series sum: Σ( z^k/(a+1)_k) k={0, inf}
/// <para>γ(a,z) = ((z^a) * (e^-z) / a) * LowerSeriesSum(a,z)</para>
/// </summary>
/// <param name="a"></param>
/// <param name="z"></param>
/// <returns></returns>
/// <see href="http://dlmf.nist.gov/8.5#E1"/>
public static double LowerSeries(double a, double z)
{
// Sum1F1 is optimized for a1 == 1
return(HypergeometricSeries.Sum1F1(1, 1 + a, z));
}
