SPENC
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
