In [8], Pierre Cartier conjectured that for any non commutative formal power series Φ on X = {x0, x1} with coefficients in a Q-extension, A, subjected to some suitable conditions, there exists an… (More)

The algebra of polylogarithms (iterated integrals over two di erential forms !0 = dz=z and !1 = dz=(1 − z)) is isomorphic to the shu e algebra of polynomials on non-commutative variables x0 and x1.… (More)

We prove that the algebra of <i>multiple harmonic sums</i> is isomorphic to a <i>shuffle algebra</i>. So the multiple harmonic sums <i>H</i><inf>s</inf>, indexed by the compositions… (More)

We present a symbolic technique for computing the exact or approximate solutions of linear di erential systems with meromorphic coe cients. To any system of that form, we attach a non-commutative… (More)

Generalized polylogarithms are de ned as iterated integrals with respect to the two di erential forms !0 = dz=z and !1 = dz=(1− z). We give an algorithm which computes the monodromy of these special… (More)

The theory of noncommutative rational power series allows to express as iterated integrals some generating series associated to polylogarithms and polyzêtas, also called MZV’s (multiple zeta values :… (More)

Ordinary generating series of multipleharmonic sums admit a full singular expansion in the basis of functions {(1 − z) log(1 − z)}α∈Z,β∈N, near the singularityz = 1. A constructiveproof of this… (More)

abstract A combinatorial study discloses two surjective morphisms between generalized shuffle algebras and algebras generated by the colored Hurwitz polyzêtas. The combinatorial aspects of the… (More)