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• W1570370571 abstract "This chapter discusses two-variable analogues of the classical orthogonal polynomials. Analogues in severable variables of the Jacobi polynomials are be highly nontrivial generalizations of the one-variable case. The chapter describes a number of distinct classes of orthogonal polynomials in two variables, for which many properties hold that are analogous to properties of Jacobi polynomials. The polynomials belonging to these orthogonal systems are eigenfunctions of two algebraically independent partial differential operators. In the Chebyshev cases, these polynomials can be interpreted as quotients of two eigenfunctions of the Laplacian on a two-dimensional torus or sphere, which satisfy symmetry relations with respect to certain reflections. The classical orthogonal polynomials in one variable are the Jacobi polynomials, the Laguerre, and the Hermite polynomials. The chapter also illustrates examples of two-variable analogues of the Jacobi polynomials." @default.
• W1570370571 created "2016-06-24" @default.
• W1570370571 creator A5087068510 @default.
• W1570370571 date "1975-01-01" @default.
• W1570370571 modified "2023-10-13" @default.
• W1570370571 title "Two-Variable Analogues of the Classical Orthogonal Polynomials" @default.
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• W1570370571 doi "https://doi.org/10.1016/b978-0-12-064850-4.50015-x" @default.
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