Evaluate a sequence of Bessel functions of the second kind with real
nonnegative order and real positive argument.
Namespace: Imsl.MathAssembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax public static double[] Y(
double xnu,
double x,
int n
)
Public Shared Function Y (
xnu As Double,
x As Double,
n As Integer
) As Double()
public:
static array<double>^ Y(
double xnu,
double x,
int n
)
static member Y :
xnu : float *
x : float *
n : int -> float[]
Parameters
- xnu
- Type: SystemDouble
A double representing the lowest order desired. xnu
must be at least zero and less than 1.
- x
- Type: SystemDouble
A double representing the argument for which the sequence
of Bessel functions is to be evaluated.
- n
- Type: SystemInt32
A int which specifies that n + 1 elements will be
evaluated in the sequence.
Return Value
Type:
Double
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
The variable xnu (represented by in
the above equation) must satisfy . If this condition is not met, then Y is set to
NaN. In addition, x must be in where and . If , then the largest representable number is returned;
and if , then zero is returned.
The algorithm is based on work of Cody and others, (see Cody et al.
1976; Cody 1969; NATS FUNPACK 1976). It uses a special series
expansion for small arguments. For moderate arguments, an analytic
continuation in the argument based on Taylor series with special
rational minimax approximations providing starting values is
employed. An asymptotic expansion is used for large arguments.
See Also