Bessel.I Method (Double, Int32)

BesselI Method (Double, Int32)

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: 6.5.2.0

Syntax

public static double[] I(
	double x,
	int n
)

Public Shared Function I ( 
	x As Double,
	n As Integer
) As Double()

public:
static array<double>^ I(
	double x, 
	int n
)

static member I : 
        x : float * 
        n : int -> float[]

Parameters

x: Type: SystemDouble
A double representing the argument of the Bessel functions to be evaluated.
n: Type: SystemInt32
The int order of the last element in the sequence.

Return Value

Type: Double
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

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.

Reference

Bessel Class

I Overload

Imsl.Math Namespace