airy_Bi
Evaluates the Airy function of the second kind.
Synopsis
#include <imsl.h>
float imsl_f_airy_Bi (float x)
The type double function is imsl_d_airy_Bi.
Required Arguments
float x (Input)
Argument for which the function value is desired.
Return Value
The Airy function of the second kind evaluated at x, Bi(x).
Description
The airy function Bi(x) is defined to be
It can also be expressed in terms of modified Bessel functions of the first kind,
Iv(
x), and Bessel functions of the first kind
Jv(
x) (see
bessel_Ix and
bessel_Jx):
and
Let
ɛ =
imsl_f_machine(4), the machine precision. If
x <
-1.31
ɛ-2/3, then the answer will have no precision. If
x <
-1 31
ɛ-1/3, the answer will be less accurate than half precision. In addition,
x should not be so large that
exp[(2/3)
x3/2] overflows. For more information, see the description for
imsl_f_machine.
Example
In this example, Bi(-4.9) is evaluated.
#include <imsl.h>
#include <stdio.h>
int main()
{
float x = -4.9;
float ans;
x = imsl_f_airy_Bi (x);
printf ("Bi(-4.9) = %f\n", x);
}
Output
Bi(-4.9) = -0.057747