In this paper, we begin by defining finite versions of the digamma and cotangent functions, and examine their Laurent or power series expansions at integer points within a certain range. By constructing contour integrals involving these finite digamma and finite cotangent functions and performing residue calculations, we derive parity results for a finite version of the double polylogarithm function. Simply taking a limit then yields the known parity formulas satisfied by cyclotomic double zeta values.
Feng et al. (Tue,) studied this question.