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


Тип публикации: статья из журнала

Год издания: 2017

Ключевые слова: 65H10, 68W30, power sums, residue integrals, Systems of transcendental equations, Waring’s formulas

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.

Ссылки на полный текст


Журнал: Complex Variables and Elliptic Equations

Номера страниц: 93-111

ISSN журнала: 17476933


  • Kytmanov A.A. (Institute of Space and Information Technology,Siberian Federal University)
  • Kytmanov A.M. (Institute of Mathematics and Computer Science,Siberian Federal University)
  • Myshkina E.K. (Institute of Mathematics and Computer Science,Siberian Federal University)

Вхождение в базы данных