Welcome to the L3 Harris Geospatial documentation center. Here you will find reference guides and help documents.
﻿

### IMSL_AIRY_AI

IMSL_AIRY_AI

The IMSL_AIRY_AI function evaluates the Airy function.

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

## 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`

## 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 (optional)

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

### DOUBLE (optional)

If present and nonzero, double precision is used.

## Version History

 6.4 Introduced