Residue integrals and Waring’s formulas for algebraic or even transcendental systems : научное издание


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

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Журнал: Complex Variables and Elliptic Equations

Номера страниц: 1-19

ISSN журнала: 17476933

Издатель: Taylor and Francis Ltd.


  • Kytmanov A.A. (Siberian Fed Univ, Inst Space & Informat Technol, Krasnoyarsk, Russia)
  • Kytmanov A.M. (Siberian Fed Univ, Inst Math & Comp Sci, Krasnoyarsk, RussiaArticle)
  • Myshkina E.K. (Siberian Fed Univ, Inst Math & Comp Sci, Krasnoyarsk, RussiaArticle)