BSJ1

This function evaluates the Bessel function of the first kind of order one.

Function Return Value-

BSJ1 — Function value. (Output)

Required Arguments

X — Argument for which the function value is desired. (Input)

FORTRAN 90 Interface

Generic: BSJ1 (X)

Specific: The specific interface names are S_BSJ1 and D_BSJ1.

FORTRAN 77 Interface

Single: BSJ1 (X)

Double: The double precision function name is DBSJ1.

Description

The Bessel function J1(x) is defined to be

 

The argument x must be zero or larger in absolute value than 2s to prevent J1(x) from underflowing. Also, ∣x∣ should be smaller than

 

to prevent the answer from being less accurate than half precision. ∣x∣ must be less than 1/ɛ for the result to have any precision at all. Here, ɛ is the machine precision, ɛ = AMACH(4), and s = AMACH(1) is the smallest representable positive floating‑point number.

Comments

Informational Error

 

Type	Code	Description
2	1	The function underflows because the absolute value of X is too small.

Example

In this example, J1(2.5) is computed and printed.

 

USE BSJ1_INT

USE UMACH_INT

 

IMPLICIT NONE

! Declare variables

INTEGER NOUT

REAL VALUE, X

! Compute

X = 2.5

VALUE = BSJ1(X)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) X, VALUE

99999 FORMAT (' BSJ1(', F6.3, ') = ', F6.3)

END

Output

 

BSJ1( 2.500) = 0.497