Evaluates the Airy function.

x—Argument for which the function value is desired.

result—The value of the Airy function evaluated at x, Ai(x).

Double—If present and nonzero, double precision is used.

Derivative—If present and nonzero, then the derivative of the Airy function is computed.

The airy function Ai(x) is defined to be:

The Bessel function Kv(x) is defined on BESSK Function (PV-WAVE Advantage).

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 (PV-WAVE Advantage)). 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.

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