Sfun.Psi1 Method

Returns the $\psi _1$ function, also known as the trigamma function.

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

Syntax

public static double Psi1(
	double x
)

Public Shared Function Psi1 ( 
	x As Double
) As Double

public:
static double Psi1(
	double x
)

static member Psi1 : 
        x : float -> float

x: Type: System.Double
A double value, the point at which the trigamma function is to be evaluated.

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

Remarks

The trigamma function, $\psi _1 (x)$ , is defined to be

$\psi _1\left(x\right)=\frac{d^2}{dx^2}\ln \Gamma(x)$

The trigamma function is not defined for integers less than or equal to zero.