This function evaluates the derivative of the Airy function of the second kind for complex arguments.
Function Return Value
CBID — 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
Aiʹ(z)
function value used to compute Biʹ(z).
(Input)
Default: SCALING = .false.
FORTRAN 90 Interface
Generic: CBID (Z)
Specific: The specific interface names are C_CBID and Z_CBID.
Description
The function Biʹ(z) is defined to be the derivative of the Airy function of the second kind, Bi(z), (see CBI), expressed using the connection formula
using function CAID for Aiʹ(z).
An optional argument, SCALING,
defines a scaling function 
that multiplies the
results. This scaling function is
|
Scaling |
Action |
|
.false. |
|
|
.true. |
|
The values for Biʹ(z) are returned with the scaling for Aiʹ(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, Biʹ(0.49, 0.49) is computed and printed.
USE CBID_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
COMPLEX Y, Z, W
! Compute
W = CMPLX(0.49,0.49)
Y = CBID(W)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99998) W, Y
!
99998 FORMAT(12x,"CBID(",F6.3 ", ",F6.3 ") = ( ",F6.3, ", ",F6.3," )" )
End
Output
CBID( 0.490, 0.490) = ( 0.411, 0.180 )
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