Sfun.Poch Method

SfunPoch Method

Returns a generalization of Pochhammer's symbol.

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

Syntax

public static double Poch(
	double a,
	double x
)

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

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

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

Parameters

a: Type: SystemDouble
A double value specifying the first argument.
x: Type: SystemDouble
A double value specifying the second, differential argument.

Return Value

Type: Double
A double value specifying the generalized Pochhammer symbol, Gamma(a+x)/Gamma(a).

Remarks

Method Poch evaluates Pochhammer's symbol $(a)_n = (a)(a - 1)\ldots (a - n + 1)$ for n a nonnegative integer. Pochhammer's generalized symbol is defined to be

$\left( a \right)_x = \frac{{\Gamma \left( {a + x} \right)}}{{\Gamma \left( a \right)}}$

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

Note that a straightforward evaluation of Pochhammer's generalized symbol with either Gamma or Log Gamma functions can be especially unreliable when a is large or x is small.

Substantial loss can occur if a + x or a are close to a negative integer unless $\left| x \right|$ is sufficiently small. To insure that the result does not overflow or underflow, one can keep the arguments a and a + x well within the range dictated by the Gamma function method Gamma or one can keep $\left| x \right|$ small whenever a is large. Poch also works for a variety of arguments outside these rough limits, but any more general limits that are also useful are difficult to specify.

Reference

Sfun Class

Imsl.Math Namespace

Other Resources

Example