Bessel.ScaledK Method

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

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

Parameters

v: A double representing the fractional order of the function. v 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

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).

Bessel.ScaledK Method

Parameters

Return Value

Remarks

See Also