期刊
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
卷 48, 期 4, 页码 1649-1665出版社
SPRINGER SINGAPORE PTE LTD
DOI: 10.1007/s41980-021-00605-8
关键词
Bivariate orthogonal polynomials; Symmetric orthogonal polynomials; Partial differential equations
类别
资金
- TUBITAK Research Grant [120F140]
- Agencia Estatal de Investigacion (AEI) of Spain [MTM2016-75140-P]
- European Community fund FEDER
- Universidade de Vigo/CISUG
A new class of partial differential equations with symmetric orthogonal solutions is introduced in this study, where orthogonality is obtained using the Sturm-Liouville approach. The general case is analyzed in detail, providing orthogonality weight function, three-term recurrence relations for monic orthogonal polynomial solutions, and explicit form of these solutions.
A new class of partial differential equations having symmetric orthogonal solutions is presented. The general equation is presented and orthogonality is obtained using the Sturm-Liouville approach. Conditions on the polynomial coefficients to have admissible partial differential equations are given. The general case is analyzed in detail, providing orthogonality weight function, three-term recurrence relations for the monic orthogonal polynomial solutions, as well as explicit form of these monic orthogonal polynomial solutions, which are solutions of an admissible and potentially self-adjoint linear second-order partial differential equation of hypergeometric type.
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