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arXiv · 1709.00791

Residue Integrals and Waring's Formulas for a Class of Systems of Transcendental Equations in $\mathbb{C}^n$

Alexey A. Kytmanov·Alexander M. Kytmanov·Evgeniya K. Myshkina
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Abstract

The present article is focused on the study of a special class of systems of nonlinear transcendental equations for which classical algebraic and symbolic methods are inapplicable. For the purpose of the study of such systems, we develop a method for computing residue integrals with integration over certain cycles. We describe conditions under which the mentioned residue integrals coincide with power sums of the inverses to the roots of a system of equations (i.e., multidimensional Waring's formulas). As an application of the suggested method, we consider a problem of finding sums of multi-variable number series.

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Alexey A. Kytmanov, Alexander M. Kytmanov, Evgeniya K. Myshkina. 2017-09-04. Residue Integrals and Waring's Formulas for a Class of Systems of Transcendental Equations in $\mathbb{C}^n$. https://arxiv.org/abs/1709.00791

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