AI

This function evaluates the Airy function.

Function Return Value

AI — Function value. (Output)

Required Arguments

X — Argument for which the Airy function is desired. (Input)

FORTRAN 90 Interface

Generic: AI (X)

Specific: The specific interface names are S_AI and D_AI.

FORTRAN 77 Interface

Single: AI (X)

Double: The double precision name is DAI.

Description

The Airy function Ai(x) is defined to be

The Bessel function K (x) is defined in BSKS.

, then the answer will have no precision. If

, the answer will be less accurate than half precision. Here, ɛ = AMACH(4) is the machine precision. Finally, x should be less than xmax so the answer does not underflow. Very approximately, xmax = {‑1.5 ln s}, where s = AMACH(1), the smallest representable positive number. If underflows are a problem for large x, then the exponentially scaled routine AIE should be used.

Comments

Informational Error

Type	Code	Description
2	1	The function underflows because X is greater than XMAX, where XMAX = (‑3/2 ln(AMACH(1))) 2∕3.

Example

In this example, Ai(–4.9) is computed and printed.

USE AI_INT

USE UMACH_INT

IMPLICIT NONE

! Declare variables

INTEGER NOUT

REAL VALUE, X

! Compute

X = -4.9

VALUE = AI(X)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) X, VALUE

99999 FORMAT (' AI(', F6.3, ') = ', F6.3)

END

Output

AI(-4.900) = 0.375