We study the Liouville equation in the domain of small deviations from absolute equilibrium. The solution is expressed in terms of amplitudes ofn-body additive functions which are orthogonal with respect to the Gibbs weight factor. In the memory operator approach the memory operators are formally exact continued fractions. We show that with the isolation in the Liouville operator of a one-body additive operatorL o, any memory operator can be written alternatively as an exact infinite series, each term of which can be calculated exactly. This yields improvements of the dressed particle approximation. We discuss the choice ofL o, which is in general time dependent. The theory is developed both for smooth potentials and for hard spheres, where we use pseudo-Liouville operators. The theory can be formulated in an equivalent manner by introducing modified cumulant distributions, which are closely related to the amplitudes. The modified cumulants have the same spatial asymptotic properties as ordinary cumulants, but have superior short-time and small-distance behavior.