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 
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 error
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, 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 )
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