BSIES
Evaluates a sequence of exponentially scaled modified Bessel functions of the first kind with nonnegative real order and real positive arguments.
Required Arguments
XNU — Real
argument which is the lowest order desired. (Input)
It must be
at least zero and less than one.
X — Real positive
argument for which the sequence of Bessel functions is to be
evaluated. (Input)
It must be nonnegative.
N — Number of elements in the sequence. (Input)
BSI — Vector of
length N
containing the values of the function through the series. (Output)
BSI(I) contains the value
of the Bessel function of order I − 1 + XNU at x for
I = 1 to N multiplied by
exp(−X).
FORTRAN 90 Interface
Generic: CALL BSIES (XNU, X, N, BSI)
Specific: The specific interface names are S_BSIES and D_BSIES.
FORTRAN 77 Interface
Single: CALL BSIES (XNU, X, N, BSI)
Double: The double precision name is DBSIES.
Description
Function BSIES
evaluates 
, for k = 1, …, n.
For the definition of Iv(x), see BSIS. The algorithm is based on a code due to
Cody (1983), which uses backward recursion.
Example
In this example, Iv−1(10.0), ν = 1, …, 10 is computed and printed.
USE BSIES_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER N
PARAMETER (N=10)
!
INTEGER K, NOUT
REAL BSI(N), X, XNU
! Compute
XNU = 0.0
X = 10.0
CALL BSIES (XNU, X, N, BSI)
! Print the results
CALL UMACH (2, NOUT)
DO 10 K=1, N
WRITE (NOUT,99999) X, XNU+K-1, X, BSI(K)
10 CONTINUE
99999 FORMAT (' exp(-', F6.3, ') * I sub ', F6.3, &
' (', F6.3, ') = ', F6.3)
END
Output
exp(-10.000) * I sub 0.000 (10.000) = 0.128
exp(-10.000) * I sub 1.000 (10.000) = 0.121
exp(-10.000) * I sub 2.000 (10.000) = 0.104
exp(-10.000) * I sub 3.000 (10.000) = 0.080
exp(-10.000) * I sub 4.000 (10.000) = 0.056
exp(-10.000) * I sub 5.000 (10.000) = 0.035
exp(-10.000) * I sub 6.000 (10.000) = 0.020
exp(-10.000) * I sub 7.000 (10.000) = 0.011
exp(-10.000) * I sub 8.000 (10.000) = 0.005
exp(-10.000) * I sub 9.000 (10.000) = 0.002
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