Evaluates a sequence of modified Bessel functions of the first kind with integer order and real argument.

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

Syntax

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

Parameters

x
Type: System..::.Double
A double representing the argument of the Bessel functions to be evaluated.
n
Type: System..::.Int32
The int order of the last element in the sequence.

Return Value

A double array of length n+1 containing the values of the function through the series.

Remarks

Bessel.I[i] contains the value of the Bessel function of order i.

The Bessel function I_n (x) is defined to be

I_n \left( x \right) = {1 \over \pi }\int_0^\pi {\,e^{x\,\cos \,\theta}} \,\cos \left( {n\,\theta } \right)\,d\,\theta

The input x must satisfy {\rm{|x| }} \le {\rm{ log(b) }} where b is the largest representable floating-point number. The algorithm is based on a code due to Sookne (1973b), which uses backward recursion.

See Also