Finding residue integrals for systems of non-algebraic equations in CnCn

A method and the corresponding algorithm of finding residue integrals for systems of non-algebraic equations containing analytic functions are presented. Such integrals are connected to the power sums of roots for a certain system of equations. The described approach can be used for developing methods for the elimination of unknowns from systems of non-algebraic equations. It is shown how the obtained results can be used for calculating sums of multidimensional series.