Sfun.Gamma Method

SfunGamma Method

Returns the Gamma function of a double.

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

Syntax

public static double Gamma(
	double x
)

Public Shared Function Gamma ( 
	x As Double
) As Double

public:
static double Gamma(
	double x
)

static member Gamma : 
        x : float -> float

Parameters

x: Type: SystemDouble
A double value.

Return Value

Type: Double
A double value specifying the Gamma function of x. If x is a negative integer, the result is NaN.

Remarks

The Gamma function, $\Gamma (x)$ , is defined to be

$\Gamma \left( x \right) = \int_0^\infty {t^{x - 1} } e^{ - t} dt \,\,\,\, for \, x \gt 0$

For $x \lt 0$ , the above definition is extended by analytic continuation.

The Gamma function is not defined for integers less than or equal to zero. Also, the argument x must be greater than so that $\Gamma (x)$ does not underflow, and x must be less than 171.64 so that $\Gamma (x)$ does not overflow. The underflow limit occurs first for arguments that are close to large negative half integers. Even though other arguments away from these half integers may yield machine-representable values of $\Gamma (x)$ , such arguments are considered illegal. Users who need such values should use the Log Gamma. Finally, the argument should not be so close to a negative integer that the result is less accurate than half precision.

$Plot of Gamma(x)$

Reference

Sfun Class

Imsl.Math Namespace

Other Resources

Example