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sub units 3.12
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MathsSpecialGamma

Gamma Lower Reg

The regularized lower incomplete Gamma integral
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GammaLower Reg

 
doublegammaLower_regdoublea
doublex )
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

ainput argument
xupper positive limit of the integral.

Authors

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

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