Some limit relationships between some two-variable finite and infinite sequences of orthogonal polynomials

Abstract

The aim of paper is to give some limit relationships between finite and infinite sequences of orthogonal polynomials in two variables and to obtain the well-known relations of some infinite sets of two-variable orthogonal polynomials by taking limit of the properties verified by finite classes of two-variable orthogonal polynomials. Furthermore, the fourth-order partial differential equations satisfied by the polynomials, which are the products of finite orthogonal polynomials, are presented and by taking limit of the derived fourth-order equations, partial differential equations for some infinite sequences of two-variable orthogonal polynomials are found.