The correlation functions of two electrostatically interacting particles have been obtained for the first time, by using the direct algebraic method for finding the cross-correlation functions. The efficiency of this method has been demonstrated by finding almost all unknown elements of the decomposition matrices in the second-order approximation.

Third-order correlation functions for two particles with the electrostatic interaction have been obtained for the first time using the direct algebraic method. The main relations for the correlation functions that do not depend on the explicit form of the interaction potential between particles, as well as the relations that appear for four specific forms of the interaction operator, are considered.