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Convergence of two-dimensional hypergeometric series for algebraic functions
Автор | Cherepanskiy, A. N. | |
Автор | Tsikh, A. K. | |
Дата внесения | 2021-08-13T09:35:02Z | |
Дата, когда ресурс стал доступен | 2021-08-13T09:35:02Z | |
Дата публикации | 2020-04 | |
Библиографическое описание | Cherepanskiy, A. N. Convergence of two-dimensional hypergeometric series for algebraic functions [Текст] / A. N. Cherepanskiy, A. K. Tsikh // Integral Transforms and Special Functions. — 2020. | |
ISSN | 10652469 | |
URI (для ссылок/цитирований) | https://www.tandfonline.com/doi/full/10.1080/10652469.2020.1756794 | |
URI (для ссылок/цитирований) | https://elib.sfu-kras.ru/handle/2311/143138 | |
Аннотация | Description of convergence domains for multiple power series is a quite difficult problem. In 1889 J.Horn showed that the case of hypergeomteric series is more favourable. He found a parameterization formula for surfaces of conjugative radii of such series. But until recently almost nothing was known about the description of convergence domains in terms of functional inequalities ρj(|a1|, . . . , |am|) < 0 relatively moduli |ai| of series variables. In this paper we give a such description for hypergeometric series representing solutions to tetranomial algebraic equations. In our study we use the remarkable observation by M. Kapranov (16) consisting in the fact that the Horn’s formulae give a parameterization of discriminant locus for a corresponding A-discriminant. We prove that usually the considered convergence domains are determined by a signle or two inequalities ρ(|at |, |as|) ≶ 0, where ρ is a reduced discriminant. | |
Тема | Hypergeometric series | |
Тема | algebraic equations | |
Тема | Horn-Kapranov parameterization | |
Тема | amoeba | |
Название | Convergence of two-dimensional hypergeometric series for algebraic functions | |
Тип | Journal Article | |
Тип | Journal Article Preprint | |
Дата обновления | 2021-08-13T09:35:02Z | |
DOI | 10.1080/10652469.2020.1756794 | |
Институт | Институт математики и фундаментальной информатики | |
Подразделение | Кафедра теории функций | |
Подразделение | Лаборатория комплексного анализа и дифференциальных уравнений | |
Журнал | Integral Transforms and Special Functions | |
Квартиль журнала в Scopus | Q2 | |
Квартиль журнала в Web of Science | Q3 |