期刊
APPLIED MATHEMATICS AND COMPUTATION
卷 325, 期 -, 页码 340-357出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2017.12.040
关键词
Orthogonal polynomials in two variables; Matrix Pearson-type equations; Matrix partial differential equations
资金
- Ministerio de Economia, Industria y Competitividad of Spain [MTM2015-65888-C4-2-P]
- European Regional Development Fund (ERDF) [MTM2014-53171-P]
- Junta de Andalucia grant [P11-FQM-7276]
We deduce new characterizations of bivariate classical orthogonal polynomials associated with a quasi-definite moment functional, and we revise old properties for these polynomials. More precisely, new characterizations of classical bivariate orthogonal polynomials satisfying a diagonal Pearson-type equation are proved: they are solutions of two separate partial differential equations one for every partial derivative, their partial derivatives are again orthogonal, and every vector polynomial can be expressed in terms of its partial derivatives by means of a linear relation involving only three terms of consecutive total degree. Moreover, we study general solutions of the matrix second order partial differential equation satisfied by classical orthogonal polynomials, and we deduce the explicit expressions for the matrix coefficients of the structure relation. Finally, some illustrative examples are given. (C) 2017 Elsevier Inc. All rights reserved.
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