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A new family of orthogonal polynomials in three variables

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A new family of orthogonal polynomials in three variables

Aktaş, Rabia; Area Carracedo, Iván Carlos; Güldoğan, Esra
 
DATE : 2020-06-16
UNIVERSAL IDENTIFIER : http://hdl.handle.net/11093/2285
UNESCO SUBJECT : 12 Matemáticas ; 1201.13 Polinomios ; Ecuaciones diferenciales
DOCUMENT TYPE : article

ABSTRACT :

In this paper we introduce a six-parameter generalization of the four-parameter three-variable polynomials on the simplex and we investigate the properties of these polynomials. Sparse recurrence relations are derived by using ladder relations for shifted univariate Jacobi polynomials and bivariate polynomials on the triangle. Via these sparse recurrence relations, second order partial differential equations are presented. Some connection relations are obtained between these polynomials. Also, new results for the four-parameter three-variable polynomials on the simplex are given. Finally, some generating functions are derived.

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