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.
If 
, 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
