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 )