Estimates of Ursell functions, group functions, and their derivatives

Estimates of the Ursell functions, truncated correlation functions and their derivatives are derived at low activity $z$ for one-component configuration system in the assumption of the smoothness of the interaction potential. As a technical tool, the results of M. Duneau, B. Souillard and D. Jagolnitzer papers [1–4] are used and their derivation is also given.