Evaluate a sequence of Bessel functions of the second kind with real nonnegative order and real positive argument.
double
representing the lowest order desired. xnu
must be at least zero and less than 1. double
representing the argument for which the sequence of Bessel functions is to be evaluated. int
which specifies that n
+ 1 elements will be evaluated in the sequence. A double
array of length n
+ 1 containing the values of the function through the series.
Bessel.K[I] contains the value of the Bessel function of order I + v at x
for I=0 to n
.
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.
Bessel Class | Imsl.Math Namespace