CBIS
Evaluates a sequence of modified Bessel functions of the first kind with real order and complex arguments.
Required Arguments
XNU — Real argument which is the lowest order desired. (Input)
XNU must be greater than –1/2.
Z — Complex argument for which the sequence of Bessel functions is to be evaluated. (Input)
N — Number of elements in the sequence. (Input)
CBS — Vector of length N containing the values of the function through the series. (Output)
CBS(I) contains the value of the Bessel function of order XNU + I ‑ 1 at Z for I = 1 to N.
FORTRAN 90 Interface
Generic: CALL CBIS (XNU, Z, N, CBS)
Specific: The specific interface names are S_CBIS and D_CBIS.
FORTRAN 77 Interface
Single: CALL CBIS (XNU, Z, N, CBS)
Double: The double precision name is DCBIS.
Description
The modified Bessel function Iv(z) is defined to be
where the Bessel function
Jv(
z) is defined in
BSJS.
This code is based on the code BESSCC of Barnett (1981) and Thompson and Barnett (1987).
For large arguments, z, Temme’s (1975) algorithm is used to find Iv(z). The Iv(z) values are recurred upward (if this is stable). This involves evaluating a continued fraction. If this evaluation fails to converge, the answer may not be accurate. For moderate and small arguments, Miller’s method is used.
Comments
Informational Errors
Type | Code | Description |
|---|
3 | 1 | One of the continued fractions failed. |
4 | 2 | Only the first several entries in CBS are valid. |
Example
In this example, I0.3+v− 1(1.2 + 0.5i), v = 1, …, 4 is computed and printed.
USE CBIS_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER N
PARAMETER (N=4)
!
INTEGER K, NOUT
REAL XNU
COMPLEX CBS(N), Z
! Compute
XNU = 0.3
Z = (1.2, 0.5)
CALL CBIS (XNU, Z, N, CBS)
! Print the results
CALL UMACH (2, NOUT)
DO 10 K=1, N
WRITE (NOUT,99999) XNU+K-1, Z, CBS(K)
10 CONTINUE
99999 FORMAT (' I sub ', F6.3, ' ((', F6.3, ',', F6.3, &
')) = (', F9.3, ',', F9.3, ')')
END
Output
I sub 0.300 (( 1.200, 0.500)) = ( 1.163, 0.396)
I sub 1.300 (( 1.200, 0.500)) = ( 0.447, 0.332)
I sub 2.300 (( 1.200, 0.500)) = ( 0.082, 0.127)
I sub 3.300 (( 1.200, 0.500)) = ( 0.006, 0.029)
