Sfun.Psi Method

SfunPsi Method

Returns the derivative of the log gamma function, also called the digamma function.

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

Syntax

public static double Psi(
	double x
)

Public Shared Function Psi ( 
	x As Double
) As Double

public:
static double Psi(
	double x
)

static member Psi : 
        x : float -> float

Parameters

x: Type: SystemDouble
A double value, the point at which the digamma function is to be evaluated.

Return Value

Type: Double
A double value specifying the logarithmic derivative of the gamma function of x. If x is a zero or a negative integer, the result is NaN. If x is too close to a negative integer the accuracy of the result will be less than half precision.

Remarks

The psi function is defined to be

$\psi(x)=\frac{d}{dx}\ln\Gamma(x)=\frac{\Gamma'(x)}{\Gamma(x)}$

See Gamma for the definition of $\Gamma(x)$ .

The argument x must not be exactly zero or a negative integer, or $\psi(x)$ is undefined. Also, x must not be too close to a negative integer such that the accuracy of the result is less than half precision.

Reference

Sfun Class

Imsl.Math Namespace

Other Resources

Example