Geodesic
Some systems of transcendental equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 137-149

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Several examples of transcendental systems of equations are considered. Since the number of roots of such systems, as a rule, is infinite, it is necessary to study power sums of the roots of negative degree. Formulas for finding residue integrals, their relation to power sums of a negative degree of roots and their relation to residue integrals (multidimensional analogs of Waring's formulas) are obtained. Calculations of multidimensional numerical series are given.
Keywords: transcendental systems of equations, power sums of roots, residue integral. 
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Alexander M. Kytmanov; Olga V. Khodos. Some systems of transcendental equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 137-149. http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a0/