Geodesic
On the usage of special functions of two variables for studying of orthogonal polynomials of two variables
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 19 (2015) no. 4, pp. 710-721

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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, consistency conditions, underrank.
Mots-clés : biorthogonal polynomials 
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     title = {On the usage of special functions of two variables for studying of orthogonal polynomials of two variables},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
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Zh. Tasmambetov. On the usage of special functions of two variables for studying of orthogonal polynomials of two variables. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 19 (2015) no. 4, pp. 710-721. http://geodesic.mathdoc.fr/item/VSGTU_2015_19_4_a9/