BSJNS
Evaluates a sequence of Bessel functions of the first kind with integer order and real or complex arguments.
Required Arguments
X — Argument for which the sequence of Bessel functions is to be evaluated. (Input)
The absolute value of real arguments must be less than 104.
The absolute value of complex arguments must be less than 104.
N — Number of elements in the sequence. (Input)
It must be a positive integer.
BS — Vector of length N containing the values of the function through the series. (Output)
BS(I) contains the value of the Bessel function of order I ‑ 1 at x for I = 1 to N.
FORTRAN 90 Interface
Generic: CALL BSJNS (X, N, BS)
Specific: The specific interface names are S_BSJNS, D_BSJNS, C_BSJNS, and Z_BSJNS.
FORTRAN 77 Interface
Single: CALL BSJNS (X, N, BS)
Double: The double precision name is DBSJNS.
Complex: The complex name is CBJNS.
Double Complex: The double complex name is DCBJNS.
Description
The complex Bessel function Jn(z) is defined to be
This code is based on the work of Sookne (1973a) and Olver and Sookne (1972). It uses backward recursion with strict error control.
Examples
Example 1
In this example, Jn(10.0), n = 0, …, 9 is computed and printed.
USE BSJNS_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER N
PARAMETER (N=10)
!
INTEGER K, NOUT
REAL BS(N), X
! Compute
X = 10.0
CALL BSJNS (X, N, BS)
! Print the results
CALL UMACH (2, NOUT)
DO 10 K=1, N
WRITE (NOUT,99999) K-1, X, BS(K)
10 CONTINUE
99999 FORMAT (' J sub ', I2, ' (', F6.3, ') = ', F6.3)
END
Output
J sub 0 (10.000) = -0.246
J sub 1 (10.000) = 0.043
J sub 2 (10.000) = 0.255
J sub 3 (10.000) = 0.058
J sub 4 (10.000) = -0.220
J sub 5 (10.000) = -0.234
J sub 6 (10.000) = -0.014
J sub 7 (10.000) = 0.217
J sub 8 (10.000) = 0.318
J sub 9 (10.000) = 0.292
Example 2
In this example, Jn(10 + 10i), n = 0, …, 10 is computed and printed.
USE BSJNS_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER N
PARAMETER (N=11)
!
INTEGER K, NOUT
COMPLEX CBS(N), Z
! Compute
Z = (10.0, 10.0)
CALL BSJNS (Z, N, CBS)
! Print the results
CALL UMACH (2, NOUT)
DO 10 K=1, N
WRITE (NOUT,99999) K-1, Z, CBS(K)
10 CONTINUE
99999 FORMAT (' J sub ', I2, ' ((', F6.3, ',', F6.3, &
')) = (', F9.3, ',', F9.3, ')')
END
Output
J sub 0 ((10.000,10.000)) = (-2314.975, 411.563)
J sub 1 ((10.000,10.000)) = ( -460.681,-2246.627)
J sub 2 ((10.000,10.000)) = ( 2044.245, -590.157)
J sub 3 ((10.000,10.000)) = ( 751.498, 1719.746)
J sub 4 ((10.000,10.000)) = (-1302.871, 880.632)
J sub 5 ((10.000,10.000)) = ( -920.394, -846.345)
J sub 6 ((10.000,10.000)) = ( 419.501, -843.607)
J sub 7 ((10.000,10.000)) = ( 665.930, 88.480)
J sub 8 ((10.000,10.000)) = ( 108.586, 439.392)
J sub 9 ((10.000,10.000)) = ( -227.548, 176.165)
J sub 10 ((10.000,10.000)) = ( -154.831, -76.050)
