Тип публикации: статья из журнала
Год издания: 2017
Идентификатор DOI: 10.1080/17476933.2017.1419210
Ключевые слова: power sums, residue integrals, Systems of transcendental equations, Waring’s formulas, 65H10, 68W30
Аннотация: The present article is focused on the study of a special class of systems of non-linear transcendental equations for which classical algebraic and symbolic methods are inapplicable. For the purpose of study of such systems we develop a method for computing residue integrals with integration over certain cycles. We describe conditioПоказать полностьюns 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). Based on this, we develop an algorithm that computes such power sums without computing the roots. As an application of the suggested method, we consider a problem of finding sums of multi-variable number series. © 2017 Informa UK Limited, trading as Taylor & Francis Group
Журнал: Complex Variables and Elliptic Equations
Номера страниц: 1-19
ISSN журнала: 17476933
Издатель: Taylor and Francis Ltd.