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A method of finding residue integrals for systems of non-algebraic equations containing analytic functions is 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.

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One approach for finding the resultant of two entire functions is discussed in the article. It is based on Newton’s recurrent formulas