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:

 

The Bessel function K_v(x) is defined on BESSK Function .

If x < -1.31e^-2/3, then the answer will have no precision. If x < -1.31e^-1/3, the answer will be less accurate than half precision. Here e is the machine precision.

x should be less than x_max so the answer does not underflow. Very approximately, x_max = {-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 < –1.31e^-2/3, then the answer will have no precision. If
x < -1.31e^-1/3, the answer will be less accurate than half precision. Here e is the machine precision. x should be less than x_max so the answer does not underflow. Very approximately, x_max = {-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