Geodesic
On transcendental systems of equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 3, pp. 326-343

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Several types of transcendental systems of equations are considered: the simplest ones, special, and general. 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. Various examples of transcendental systems of equations and calculation 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. On transcendental systems of equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 3, pp. 326-343. http://geodesic.mathdoc.fr/item/JSFU_2021_14_3_a5/