This function evaluates the Kelvin function of the second kind, kei, of order zero.

Function Return Value

AKEI0 — Function value.   (Output)

Required Arguments

X — Argument for which the function value is desired.   (Input)
It must be nonnegative and less than 119.

FORTRAN 90 Interface

Generic:                              AKEI0 (X)

Specific:                             The specific interface names are S_AKEI0 and D_AKEI0.

FORTRAN 77 Interface

Single:                                AKEI0 (X)

Double:                              The double precision name is DKEI0.

Description

The modified Kelvin function kei0(x) is defined to be ℑK0(xeπi∕4). The Bessel function K0(x) is defined in BSK0. Function AKEI1 is based on the work of Burgoyne (1963).

In AKEI0, x must satisfy 0 ≤ x < 119. If x < 0, then NaN (not a number) is returned. If x ≥ 119, then zero is returned.

Example

In this example, kei0(0.4) is computed and printed.

 

      USE AKEI0_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    NOUT

      REAL       VALUE, X

!                                 Compute

      X     = 0.4

      VALUE = AKEI0(X)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) X, VALUE

99999 FORMAT (' AKEI0(', F6.3, ') = ', F6.3)

      END

Output

 

AKEI0( 0.400) = -0.704

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