This function evaluates a form of Spence's integral.

Function Return Value

SPENC — Function value.   (Output)

Required Arguments

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

FORTRAN 90 Interface

Generic:                              SPENC (X)

Specific:                             The specific interface names are S_SPENC and D_SPENC.

FORTRAN 77 Interface

Single:                                SPENC (X)

Double:                              The double precision function name is DSPENC.

Description

The Spence dilogarithm function, s(x), is defined to be

 

For |x| ≤ 1, the uniformly convergent expansion

 

is valid.

Spence's function can be used to evaluate much more general integral forms. For example,

 

Example

In this example, s(0.2) is computed and printed.

 

      USE SPENC_INT

      USE UMACH_INT

 

      IMPLICIT    NONE

!                                 Declare variables

      INTEGER    NOUT

      REAL       VALUE, X

!                                 Compute

      X     = 0.2

      VALUE = SPENC(X)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) X, VALUE

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

      END

Output

 

SPENC( 0.200) =  0.211

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