CBI
This function evaluates the Airy function of the second kind for complex arguments.
Function Return Value
CBI — Complex function value. (Output)
Required Arguments
Z — Complex argument for which the Airy function value is desired. (Input)
Optional Arguments
SCALING — Logical argument specifying whether or not the scaling function will be applied to the Ai(z) function value used to compute Bi(z). (Input)
Default: SCALING = .false.
FORTRAN 90 Interface
Generic: CBI (Z)
Specific: The specific interface names are C_CBI and Z_CBI.
Description
The Airy function of the second kind Bi(z) is expressed using the connection formula
using function CAI for Ai(z).
An optional argument, SCALING, defines a scaling function s(z) that multiplies the results. This scaling function is
Scaling
Action
.false.
.true.
The values for Bi(z) are returned with the scaling for Ai(z).
Comments
Informational Errors
Type
Code
Description
2
1
The real part of (2/3) × Z(32) 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(32) 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, Bi(0.49, 0.49) is computed and printed.
 
USE CBI_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
COMPLEX Y, Z, W
! Compute
W = CMPLX(0.49,0.49)
Y = CBI(W)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99998) W, Y
!
99998 FORMAT(12x,"CBI(",F6.3 ", ",F6.3 ") = ( ",F6.3, ", ",F6.3," )" )
End
Output
 
CBI( 0.490, 0.490) = ( 0.802, 0.243 )