Evaluate a sequence of Bessel functions of the first kind with real order and real positive argument.

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

Syntax

C#
public static double[] J(
	double xnu,
	double x,
	int n
)
Visual Basic (Declaration)
Public Shared Function J ( _
	xnu As Double, _
	x As Double, _
	n As Integer _
) As Double()
Visual C++
public:
static array<double>^ J(
	double xnu, 
	double x, 
	int n
)

Parameters

xnu
Type: System..::.Double
A double representing the lowest order desired. xnu must be at least zero and less than 1.
x
Type: System..::.Double
A double representing the argument for which the sequence of Bessel functions is to be evaluated.
n
Type: System..::.Int32
A int representing the order of the last element in the sequence. If order is the highest order desired, set n to int(order).

Return Value

A double array of length n+1 containing the values of the function through the series. Bessel.J[I] contains the value of the Bessel function of order I + v at x for I=0 to n.

Remarks

The Bessel function J_v (x), is defined to be

J_\nu (x) = {{(x/2)^\nu } \over {\sqrt \pi \Gamma (\nu + 1/2)}}\int_0^\pi {\,\,\cos \left( {x\,\cos \,\theta } \right)\sin ^{2\nu } \theta \,\,d\,\theta }

This code is based on the work of Gautschi (1964) and Skovgaard (1975). It uses backward recursion.

See Also