airy_Ai_derivative
Evaluates the derivative of the Airy function.
Synopsis
#include <imsl.h>
float imsl_f_airy_Ai_derivative (float x)
The type double function is imsl_d_airy_Ai_derivative.
Required Arguments
float x (Input)
Argument for which the function value is desired.
Return Value
The derivative of the Airy function.
Description
The airy function Ai
′(
x) is defined to be the derivative of the Airy function, Ai(
x). 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. Here
ɛ =
imsl_f_machine(4) is the machine precision. Finally,
x should be less than
xmax so that the answer does not underflow. Very approximately,
xmax = {
-1.51ln
s}, where
s =
imsl_f_machine(1), the smallest representable positive number. For more information, see the description for
imsl_f_machine.
Example
In this example, Ai′(-4.9) is evaluated.
#include <imsl.h>
#include <stdio.h>
int main()
{
float x = -4.9;
float ans;
x = imsl_f_airy_Ai_derivative (x);
printf ("Ai’(-4.9) = %f\n", x);
}
Output
Ai’(-4.9) = 0.146958