Integral representation of the group operation of the local Lie group. The reduced form of the Campbell-Hausdorff series

We obtain the parametric solution of the system of Lie differential equations in the first kind canonical coordinates using the given structural constants. After complexification via Yuzhakov formulas we obtain the integral representation of the group operation of the local Lie group and the reduced form of the Campbell-Hausdorff series. We consider the example.
Keywords: multiple logarithmic residue, implicit function theorem in several complex variables, canonical coordinates of the first kind, Dynkin's form of the Campbell-Hausdorff series.