  The problem considered is the computation of an infinite product
(composition) of Lie transformations generated by homogeneous polynomials of
increasing order from a given convergent power series. Bounds are computed for
the infinitesimal form of Lie transformations. The results obtained do not
guarantee convergence of the product. Instead, the optimum truncation is
determined by minimizing the terms of order n+1 that remain after the first n
Lie transformations have been applied.
