Monomial and Rodrigues orthogonal polynomials on the cone

Abstract

We study two families of orthogonal polynomials with respect to some weight on the cone. The first family are monomials polynomials and we provide an explicit constructions them. The second family consists of orthogonal polynomials defined by the Rodrigues type formula when the scalar measure defining our measure on the cone is the Laguerre or the Jacobi weight, which satisfies a generating function in both cases. The two families of polynomials are partially biorthogonal.