CAI
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 s(z) that multiplies the results. This scaling function is
Scaling | Action |
|---|
.false. | |
.true. | |
Comments
Informational Errors
Type | Code | Description |
|---|
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 )
