IMSL_AIRY_AI

Syntax | Return Value | Arguments | Keywords | Discussion | Example | Version History

The IMSL_AIRY_AI function evaluates the Airy function.

Note
This routine requires an IDL Advanced Math and Stats license. For more information, contact your ITT Visual Information Solutions sales or technical support representative.

Syntax

Result = IMSL_AIRY_AI(x [, DERIVATIVE=value] [, /DOUBLE])

Return Value

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

Arguments

x

Argument for which the function value is desired.

Keywords

DERIVATIVE

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

DOUBLE

If present and nonzero, double precision is used.

Discussion

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

The Bessel function K_v(x) is defined in IMSL_BESSK.

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 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 IMSL_AIRY_AI). 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 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, IMSL_AIRY_AI(-4.9) 
     0.374536  
PRINT, IMSL_AIRY_AI(-4.9, /Derivative)     
     0.146958 

Version History