Siberian Federal University

Examples of computing power sums of roots of systems of equations, including transcenden- tal, are considered. Since the number of roots of such systems is, as a rule, infinite, it is necessary to study the power sums of roots in a negative degree. Formulas for finding residue integrals, their con- nection with power sums of roots to a negative degree, multidimensional analogues of Waring’s formulas are given