Drinfel’d associator and relations of some special functions

We observe the differential equation dG(z) / dz = (x0 z + x1 (1- z))G(z) in space of power series noncommutative indeterminates x0, , where coefficients G(z) are holomorphic functions on simply connected domain ℂ \ [(-∞,0)∪(1,+∞)].Researches this some conditions turn out different solutions which admit Drinfel'd associator as a bridge. In paper, we review representations these by generating special such multiple harmonic sums, polylogarithms and polyzetas. Thereby, relations explicit forms or asymptotic expansions from bridge equations deduced identifying local coordinates.