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Differential Equations and Mathematical Physics
On the usage of special functions of two variables for studying of orthogonal polynomials of two variables
Zh. Tasmambetov Aktobe State University after K. Zhubanov, Aktobe, 030000, Kazakhstan
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
It is shown that the second order partial differential equations system defined by author is the most general system. It is possible to get all systems, solutions of which are hypergeometric functions of two variables from a Horn list and biorthogonal systems of Hermite and Appel polynomials. In this case the main apparatus of biorthogonal polynomials of two variables study is special functions of two variables. The resulting system of hypergeometric type allows us to use unified approach for the construction of biorthogonal systems of polynomials. All possible singular curves of the studied system are set. The existence of regular solutions is set by Frobenius–Latysheva method.
Keywords:
singular curves, hypergeometric type system, biorthogonal polynomials, consistency conditions, underrank.
Original article submitted 11/I/2015 revision submitted – 27/V/2015
Citation:
Zh. Tasmambetov, “On the usage of special functions of two variables for studying of orthogonal polynomials of two variables”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:4 (2015), 710–721
Linking options:
https://www.mathnet.ru/eng/vsgtu1399 https://www.mathnet.ru/eng/vsgtu/v219/i4/p710
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Abstract page: | 357 | Full-text PDF : | 229 | References: | 75 |
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