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 < -1.31ɛ-2/3, then the answer will have no precision. If x < -1 31ɛ-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