AIRY_AI Function
Evaluates the Airy function.
Usage
result = AIRY_AI(x)
Input Parameters
x—Argument for which the function value is desired.
Returned Value
result—The value of the Airy function evaluated at x, Ai(x).
Input Keywords
Double—If present and nonzero, double precision is used.
Derivative—If present and nonzero, then the derivative of the Airy function is computed.
Discussion
The airy function Ai(x) is defined to be:
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 is the machine precision.
x should be less than xmax so the answer does not underflow. Very approximately, xmax = {−1.5lns}2/3, where s = the smallest representable positive number.
If the keyword Derivative is set, then the airy function Ai'(x) is defined to be the derivative of the Airy function, Ai(x) (see the AIRY_AI Function). 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 is the machine precision. x should be less than xmax so the answer does not underflow. Very approximately, xmax = {−1.51lns}, where s is the smallest representable positive number.
x < −1.31ε-1/3, the answer will be less accurate than half precision. Here ε is the machine precision. x should be less than xmax so the answer does not underflow. Very approximately, xmax = {−1.51lns}, where s is the smallest representable positive number.
Example
In this example, Ai(–4.9) and Ai'(–4.9) are evaluated.
PRINT, AIRY_AI(-4.9)
; PV-WAVE prints: 0.374536
PRINT, AIRY_AI(-4.9, /Derivative)
; PV-WAVE prints: 0.146958
