This function evaluates the modified Bessel function of the second kind of order one.

Function Return Value

BSK1 — Function value.   (Output)

Required Arguments

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

FORTRAN 90 Interface

Generic:                              BSK1 (X)

Specific:                             The specific interface names are S_BSK1 and D_BSK1.

FORTRAN 77 Interface

Single:                                BSK1 (X)

Double:                              The double precision function name is DBSK1.

Description

The Bessel function K1(x) is defined to be

The argument x must be large enough (> max(1/b, s)) that K1(x) does not overflow, and x must be small enough that the approximate answer,

does not underflow. Here, s is the smallest representable positive floating-point number, s = AMACH(1) , and b = AMACH(2) is the largest representable floating-point number.

Comments

Informational error

Type Code

2         1                  The function underflows because X is too large.

Example

In this example, K1(0.5) is computed and printed.

 

      USE BSK1_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    NOUT

      REAL       VALUE, X

!                                 Compute

      X     = 0.5

      VALUE = BSK1(X)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) X, VALUE

99999 FORMAT (' BSK1(', F6.3, ') = ', F6.3)

      END

Output

 

BSK1( 0.500) =  1.656

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