Bessel.K Method (Double, Double, Int32)

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

public static double[] K(
   double xnu,
   double x,
   int n
);

Parameters

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

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).

Bessel.K Method (Double, Double, Int32)

Parameters

Return Value

Remarks

See Also