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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
)

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)
See Also