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

Autor:	Kytmanov, Alexey A., Kytmanov, Alexander M., Myshkina, Evgeniya K.
Rok vydání:	2017
Předmět:	Mathematics - Complex Variables 65H10 68W30
Druh dokumentu:	Working Paper
Popis:	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. Comment: 19 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1709.00791 Zobrazit plný text záznamu View this record from Arxiv