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.

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

Additional Example

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)

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