Computes the normalized lower (left) incomplete Gamma function.

Namespace:  Meta.Numerics.Functions
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 1.5.0.0 (1.5.0.0)

Syntax

         
 C#  Visual Basic  Visual C++ 
public static double LeftGamma(
	double a,
	double x
)
Public Shared Function LeftGamma ( _
	a As Double, _
	x As Double _
) As Double
public:
static double LeftGamma(
	double a, 
	double x
)

Parameters

a
Double
The shape parameter, which must be positive.
x
Double
The argument, which must be non-negative.

Return Value

The value of γ(a,x)/Γ(x).

Remarks

The incomplete Gamma function is obtained by carrying out the Gamma function integration from zero to some finite value x, instead of to infinity. The function is normalized by dividing by the complete integral, so the function ranges from 0 to 1 as x ranges from 0 to infinity.

For large values of x, this function becomes 1 within floating point precision. To determine its deviation from 1 in this region, use the complementary function RightGamma(Double, Double).

For a=ν/2 and x=χ2/2, this function is the CDF of the χ2 distribution with ν degrees of freedom.

Exceptions

See Also