The IMSL_AIRY_AI function evaluates the Airy function.

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

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

See Also

IMSL_AIRY_BI, IMSL_BESSK