Abstract:
Examples of computing power sums of roots of systems of equations, including transcendental, 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 connection with power sums of roots to a negative degree, multidimensional analogues of Waring's formulas are given.
Keywords:transcendental systems of equations, power sums of roots, residue integrals.
UDC:519.6
Received: 23.10.2022 Received in revised form: 14.11.2022 Accepted: 15.12.2022