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.

中文翻译：

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三个变量的正交多项式的新族

在本文中，我们在单纯形上介绍了四参数三变量多项式的六参数泛化，并研究了这些多项式的性质。稀疏递归关系是通过对梯形上的移位一元Jacobi多项式和二元多项式使用梯形关系得出的。通过这些稀疏递归关系，给出了二阶偏微分方程。在这些多项式之间获得了一些连接关系。此外，给出了单纯形上四参数三变量多项式的新结果。最后，导出一些生成函数。