Orthogonal polynomials of several variables

Abstract

This is Chapter 2 for Volume 2, entitled {\it Multivariable special functions}, of the Askey-Bateman project. We provide an overview of the basic results on orthogonal polynomials of several variables. After a short introduction on general properties, the main text concentrates on specific systems of orthogonal polynomials in two and more variables that correspond to, or are generalizations of, classical orthogonal polynomials of one variable.