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, ε = AMACH(4) is the machine precision. Finally, x should be less than  so the answer does not underflow. Very approximately, , 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

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

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