This function evaluates the Airy function of the first kind for complex arguments.
Function Return Value
CAI — Complex function value. (Output)
Required Arguments
Z — Complex argument for which the Airy function is desired. (Input)
Optional Arguments
SCALING — Logical
argument specifying whether or not the scaling function will be applied to the
Ai(z) function value. (Input)
Default: SCALING = .false.
FORTRAN 90 Interface
Generic: CAI (Z)
Specific: The specific interface names are C_CAI and Z_CAI.
Description
The Airy function Ai(z) is a solution of the
differential equation
. The
mathematical development and algorithm, 838, used here are found in the work by
Fabijonas et al. Function CAI
returns the complex values of Ai(z).
An optional argument, SCALING,
defines a scaling function 
that multiplies the results. This
scaling function is
|
Scaling |
Action |
|
.false. |
|
|
.true. |
|
Comments
Type Code
2 1 The real part of (2/3) × Z(3∕2) was too large in the region where the function is exponentially small; function values were set to zero to avoid underflow. Try supplying the optional argument SCALING.
2 2 The real part of (2/3) × Z(3∕2) was too large in the region where the function is exponentially large; function values were set to zero to avoid underflow. Try supplying the optional argument SCALING.
Example
In this example, Ai(0.49, 0.49) is computed and printed.
USE CAI_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
COMPLEX Y, Z, W
! Compute
W = CMPLX(0.49,0.49)
Y = CAI(W)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99998) W, Y
!
99998 FORMAT(12x,"CAI(",F6.3 ", ",F6.3 ") = ( ",F6.3, ", ",F6.3," )" )
End
Output
CAI( 0.490, 0.490) = ( 0.219, -0.113 )
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