Some New Families of Finite Orthogonal Polynomials in Two Variables

In this paper, we generalize the study of finite sequences of orthogonal polynomials from one to two variables. In doing so, twenty three new classes of bivariate finite orthogonal polynomials are presented, obtained from the product of a finite and an infinite family of univariate orthogonal polynomials. For these new classes of bivariate finite orthogonal polynomials, we present a bivariate weight function, the domain of orthogonality, the orthogonality relation, the recurrence relations, the second-order partial differential equations, the generating functions, as well as the parameter derivatives. The limit relations among these families are also presented in Labelle's flavor.

Automated summary

This paper generalizes the study of finite sequences of orthogonal polynomials from one to two variables and presents twenty three new classes of bivariate finite orthogonal polynomials. Various properties of these polynomial classes, including weight function, domain of orthogonality, recurrence relations, partial differential equations, etc., are introduced.