Evaluates the Airy function.
Synopsis
#include <imsl.h>
float imsl_f_airy_Ai (float x)
The type double function is imsl_d_airy_Ai.
Required Arguments
float x
(Input)
Argument for which the function value is desired.
Return Value
The Airy function evaluated at x, Ai(x).
Description
The airy function Ai(x) is defined to be
The Bessel function Kv(x) is defined in bessel_exp_K0.
If x < −1.31ε-2/3, then the answer will have no precision. If x < −1.31ε-1/3, the answer will be less accurate than half precision. Here ε = imsl_f_machine(4) is the machine precision.
Finally, x should be less than xmax so the answer does not underflow. Very approximately, xmax = {−1.5lns}2/3, where s = imsl_f_machine(1), the smallest representable positive number.
Example
In this example, Ai(−4.9) is evaluated.
#include <imsl.h>
int main()
{
float x = -4.9;
float ans;
x = imsl_f_airy_Ai (x);
printf ("Ai(-4.9) = %f\n", x);
}
Output
Ai(-4.9) = 0.374536
