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

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

Syntax

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

Parameters

xnu
Type: System..::.Double
A double representing the fractional order of the function. xnu must be less than one in absolute value.
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.

Remarks

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

The Bessel function K_v (x) is defined to be

K_\nu (x) = \frac{\pi}{2}e^{\nu \pi i/2} \left[ {i\,J_\nu (ix) - Y_\nu (ix)} \right] \,\,\,\, \rm{for} - \pi \lt \arg \,x \le \frac{\pi}{2}

Currently, xnu (represented by \nu in the above equation) is restricted to be less than one in absolute value. A total of n values is stored in the result, K.

K\left[ {\rm{0}} \right] = K_v (x), K\left[ {\rm{1}} \right] = K_{v + 1} (x), \ldots, K \left[ {n - 1} \right] = K_{v + n - 1} (x).

This method is based on the work of Cody (1983).

See Also