Gamma Lower Reg

Dependents

this module uses 2 subunits Log_GammaMachine_Epsilon

Interface

GammaLower Reg

The regularized lower portion of the incomplete Gamma integral. This is also sometime referred to as the left tail of the integral, i.e

Accuracy:

Tested at random a, x.

Relative error:
domain     # trials      peak         rms
0,30       200000       3.6e-14     2.9e-15
0,100      300000       9.9e-14     1.5e-14

Example:

#include <stdio.h>
#include <codecogs/maths/special/gamma/gamma_lower_reg.h>
void main
{
  for(double a=0; a<3; a+=0.25)
  {
    double y=Maths::Special::Gamma::gammaLower_reg(a, 2);
    printf("\n gammaLower_reg(%lf, 2)=%lf", a,y);
  }
}

Output:

gammaLower_reg(0.000000, 2)=1.000000
gammaLower_reg(0.250000, 2)=0.982714
gammaLower_reg(0.500000, 2)=0.954500
gammaLower_reg(0.750000, 2)=0.914944
gammaLower_reg(1.000000, 2)=0.864665
gammaLower_reg(1.250000, 2)=0.805153
gammaLower_reg(1.500000, 2)=0.738536
gammaLower_reg(1.750000, 2)=0.667294
gammaLower_reg(2.000000, 2)=0.593994
gammaLower_reg(2.250000, 2)=0.521056
gammaLower_reg(2.500000, 2)=0.450584
gammaLower_reg(2.750000, 2)=0.384266

References:

Cephes Math Library Release 2.8: June, 2000

Note

In this implementation, both parameters must be positive.

Parameters

a	input argument
x	upper positive limit of the integral.

Authors

Stephen L.Moshier. Copyright 1984, 1987, 1989, 1992, 2000
Documented and Updated by Will Bateman

Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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