BSIS

Evaluates a sequence of modified Bessel functions of the first kind with real order and real positive arguments.

Required Arguments

XNU — Real argument which is the lowest order desired. (Input)
It must be greater than or equal to zero and less than one.

X — Real argument for which the sequence of Bessel functions is to be evaluated. (Input)

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.

FORTRAN 90 Interface

Generic: CALL BSIS (XNU, X, N, BSI)

Specific: The specific interface names are S_BSIS and D_BSIS.

FORTRAN 77 Interface

Single: CALL BSIS (XNU, X, N, BSI)

Double: The double precision name is DBSIS.

Description

The Bessel function Iv(x) is defined to be

 

The input x must be nonnegative and less than or equal to log(b) (b = AMACH(2), the largest representable number). The argument v = XNU must satisfy 0 ≤ v ≤ 1.

Function BSIS is based on a code due to Cody (1983), which uses backward recursion.

Example

In this example, Iv−1(10.0), v = 1, …, 10 is computed and printed.

 

USE BSIS_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 BSIS (XNU, X, N, BSI)

! Print the results

CALL UMACH (2, NOUT)

DO 10 K=1, N

WRITE (NOUT,99999) XNU+K-1, X, BSI(K)

10 CONTINUE

99999 FORMAT (' I sub ', F6.3, ' (', F6.3, ') = ', F10.3)

END

Output

 

I sub 0.000 (10.000) = 2815.717

I sub 1.000 (10.000) = 2670.988

I sub 2.000 (10.000) = 2281.519

I sub 3.000 (10.000) = 1758.381

I sub 4.000 (10.000) = 1226.491

I sub 5.000 (10.000) = 777.188

I sub 6.000 (10.000) = 449.302

I sub 7.000 (10.000) = 238.026

I sub 8.000 (10.000) = 116.066

I sub 9.000 (10.000) = 52.319