This function evaluates the derivative of the Airy function.

Function Return Value

AID — Function value.   (Output)

Required Arguments

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

FORTRAN 90 Interface

Generic:                              AID (X)

Specific:                             The specific interface names are S_AID and D_AID.

FORTRAN 77 Interface

Single:                                AID (X)

Double:                              The double precision name is DAID.

Description

The function Aiʹ(x) is defined to be the derivative of the Airy function, Ai(x) (see AI).

If x < -1.31 ε−2∕3, then the answer will have no precision. If x < -1.31 ε−1∕3, the answer will be less accurate than half precision. Here, ε = AMACH(4) is the machine precision. Finally, x should be less than x∀ so that the answer does not underflow. Very approximately, x∀ = {-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 AIDE 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)).

Example

In this example, Aiʹ(-4.9) is computed and printed.

 

      USE AID_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    NOUT

      REAL       VALUE, X

!                                 Compute

      X     = -4.9

      VALUE = AID(X)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) X, VALUE

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

      END

Output

 

AID(-4.900) = 0.147

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