A new family of orthogonal polynomials in three variables

Journal of inequalities and applications

article

Rabia Aktaş¹  Iván Area²  Esra Güldoğan³ 

[1] Department of Mathematics, Faculty of Science, Ankara University;Universidade de Vigo;Department of Mathematics, Atilim University

关键词: Jacobi polynomials;    Koornwinder polynomials;    Generating function;    Recurrence relation;    Partial differential equation;    Connection relation;   

DOI  :  10.1186/s13660-020-02434-5

学科分类：电力

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY