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 < -1.31ɛ-2/3, then the answer will have no precision. If x < -1.31ɛ-1/3, the answer will be less accurate than half precision. 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 = {-1.51lns}, 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