Evaluates a sequence of 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 CBJS (XNU, Z, N, CBS)
Specific: The specific interface names are S_CBJS and D_CBJS.
FORTRAN 77 Interface
Single: cALL CBJS (XNU, Z, N, CBS)
Double: The double precision name is DCBJS.
Description
The Bessel function Jν(z) is defined to be
This code is based on the code BESSCC of Barnett (1981) and Thompson and Barnett (1987).
This code computes Jν(z) from the modified Bessel function Iν(z), CBIS, using the following relation, with ρ = ei π∕2:
Comments
Informational error
Type Code
3 1 One of the continued fractions failed.
4 2 Only the first several entries in CBS are valid.
Example
In this example, J0.3+ ν−1(1.2 + 0.5i), ν= 1, …, 4 is computed and printed.
USE CBJS_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 CBJS (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 (' J sub ', F6.3, ' ((', F6.3, ',', F6.3, &
')) = (', F9.3, ',', F9.3, ')')
END
Output
J sub 0.300 (( 1.200, 0.500)) = ( 0.774, -0.107)
J sub 1.300 (( 1.200, 0.500)) = ( 0.400, 0.159)
J sub 2.300 (( 1.200, 0.500)) = ( 0.087, 0.092)
J sub 3.300 (( 1.200, 0.500)) = ( 0.008, 0.024)
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