Evaluate a sequence of exponentially scaled modified Bessel functions
of the third kind with fractional order and real argument.
Namespace: Imsl.MathAssembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax 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
,
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 must not be
zero, and
x must be greater than zero.
must be less than 1. Also, when
is large compared with x,
must not be so large that
overflows. The code
is based on work of Cody (1983).
See Also