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Residue integrals and Waring's formulas for algebraic or even transcendental systems
| Content Provider | Scilit |
|---|---|
| Author | Kytmanov, A. A. Myshkina, E. K. |
| Copyright Year | 2017 |
| Description | 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 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). 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. |
| Related Links | http://elib.sfu-kras.ru/bitstream/2311/111520/1/kkm_2017_postprint.pdf |
| ISSN | 17476933 |
| e-ISSN | 17476941 |
| DOI | 10.1080/17476933.2017.1419210 |
| Journal | Complex Variables and Elliptic Equations |
| Issue Number | 1 |
| Volume Number | 64 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2019-01-02 |
| Access Restriction | Open |
| Subject Keyword | Journal: Complex Variables and Elliptic Equations Literary Studies Systems of Transcendental Equations Residue Integrals Power Sums Waring's Formulas 65h10 68w30 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Analysis Computational Mathematics Numerical Analysis |
