Bessel.ScaledK Method

BesselScaledK Method

Evaluate a sequence of exponentially scaled modified Bessel functions of the third kind with fractional order and real argument.

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

Syntax

C++

Copy

public static double[] ScaledK(
	double v,
	double x,
	int n
)

Public Shared Function ScaledK ( 
	v As Double,
	x As Double,
	n As Integer
) As Double()

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

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

Parameters

v: Type: SystemDouble
A double representing the fractional order of the function. v must be less than one in absolute value.
x: Type: SystemDouble
A double representing the argument for which the sequence of Bessel functions is to be evaluated.
n: Type: SystemInt32
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

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

Remarks

If n is positive, Bessel.K[I] contains times the value of the Bessel function of order I + v at x for I = 0 to n.

If n is negative, Bessel.K[I] contains times the value of the Bessel function of order v - I at x for I = 0 to n.

This function evaluates $e^x K_{\nu + i -1} (x)$ , for i=1,...,n where K is the modified Bessel function of the third kind. Currently, v is restricted to be less than 1 in absolute value. A total of

elements are returned in the array. This code is particularly useful for calculating sequences for large x provided n = x. (Overflow becomes a problem if $n \lt \lt x$ .) n must not be zero, and x must be greater than zero. $|\nu|$ must be less than 1. Also, when

is large compared with x,

must not be so large that

$e^x K_{\nu+n}(x) = e^x \frac{\Gamma(|\nu+n|)}{2(x/2)^{\nu+n}}$

overflows. The code is based on work of Cody (1983).

Reference

Bessel Class

Imsl.Math Namespace