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This article is cited in 2 scientific papers (total in 2 papers)
Analytic continuation for solutions to the system of trinomial algebraic equations
Irina A. Antipova, Ekaterina A. Kleshkova, Vladimir R. Kulikov Siberian Federal University, Krasnoyarsk, Russian Federation
Abstract:
In the paper, we deal with the problem of getting analytic continuations for the monomial function associated with a solution to the reduced trinomial algebraic system.
In particular, we develop the idea of applying the Mellin–Barnes integral representation of the monomial function for solving the extension problem and demonstrate how to achieve the same result following the fact that the solution to the universal trinomial system is polyhomogeneous. As a main result, we construct Puiseux expansions (centred at the origin) representing analytic continuations of the monomial function.
Keywords:
algebraic equation, analytic continuation, Puiseux series, discriminant locus, Mellin–Barnes integral.
Received: 05.10.2019 Received in revised form: 09.11.2019 Accepted: 24.12.2019
Citation:
Irina A. Antipova, Ekaterina A. Kleshkova, Vladimir R. Kulikov, “Analytic continuation for solutions to the system of trinomial algebraic equations”, J. Sib. Fed. Univ. Math. Phys., 13:1 (2020), 114–130
Linking options:
https://www.mathnet.ru/eng/jsfu824 https://www.mathnet.ru/eng/jsfu/v13/i1/p114
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Abstract page: | 259 | Full-text PDF : | 113 | References: | 37 |
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