Orthogonal polynomials of two discrete variables on the simplex

Abstract

In this article, a method for constructing families of orthogonal polynomials of two discrete variables on the triangle is presented. Some examples, related with Hahn, Meixner, Kravchuk and Charlier polynomials, are discussed in detail, giving recurrence relation in vector–matrix form for the orthonormal families, partial difference equation, limit relations between them, as well as forward and backward structure relations. Finally, as a limit case of Hahn polynomials of two variables we recover the Jacobi polynomials of two variables on the triangle.

Keywords:

• Multivariable orthogonal polynomials

Acknowledgements

This work was partially supported by Ministerio de Ciencia y Tecnología of Spain under grants BFM2001–3423 and BFM2002–04315–C02–01.