Sfun.GammaIncomplete Method

SfunGammaIncomplete Method

Evaluates the incomplete gamma function.

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

public static double GammaIncomplete(
	double a,
	double x
)

Public Shared Function GammaIncomplete ( 
	a As Double,
	x As Double
) As Double

public:
static double GammaIncomplete(
	double a, 
	double x
)

static member GammaIncomplete : 
        a : float * 
        x : float -> float

Parameters

a: Type: SystemDouble
A double value representing the integrand exponent parameter of the incomplete gamma function. If a is less than zero a Double.NaN is returned. equal to zero.
x: Type: SystemDouble
A double value specifying the point at which the incomplete gamma function is to be evaluated. If x is less than zero or equal to zero, Double.NaN or 0.0 respectively is returned. nonnegative.

Return Value

Type: Double
A double value specifying the incomplete gamma function.

Remarks

The lower limit of integration of the incomplete gamma function, $\gamma(a,x)$ , is defined to be

$\gamma(a,x)=\int_{0}^{x}t^{a-1}e^{-t}dt\;\;\;\; \mbox{for }x\ge0\mbox{ and }a>0$

Although $\gamma(a,x)$ is well defined for $x>-\infty$ , this algorithm does not calculate $\gamma(a,x)$ for negative x. For large a and sufficiently large x, $\gamma(a,x)$ may overflow. $\gamma(a,x)$ is bounded by $\Gamma(a)$ , and users may find this bound a useful guide in determining legal values for a.

Note that the upper limit of integration of the incomplete gamma, $\Gamma(a,x)$ , is defined to be

$\Gamma(a,x)=\int_{x}^{\infty}t^{a-1}e^{-t}dt$

Therefore, by definition, the two incomplete gamma function forms satisfy the relationship

$\Gamma(a,x)+\gamma(a,x)=\Gamma(a)$

Reference

Sfun Class

Imsl.Math Namespace