Returns a generalization of Pochhammer's symbol.

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
public static double Poch(
	double a,
	double x
)
Visual Basic (Declaration)
Public Shared Function Poch ( _
	a As Double, _
	x As Double _
) As Double
Visual C++
public:
static double Poch(
	double a, 
	double x
)

Parameters

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

Return Value

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.

See Also