On Koornwinder classical orthogonal polynomials in two variables

Matrix Pearson Equations Satisfied by Koornwinder Weights in Two Variables

“…Observe that the tensor product of two monic orthogonal polynomials in one variable Now, we will recover a Theorem in [7] where it was proved that the semiclassical character is inherited by bivariate Koornwinder polynomials Theorem 3 ([7]). Let w 1 and w 2 be two semiclassical weight functions in one variable.…”

“…Recently, in [7], the authors studied the Koornwinder's construction in a more general framework. They deduced some additional properties for weight functions associated with this polynomials and introduced some new examples of bivariate Koornwinder polynomials.…”

“…In this work, we study bivariate Koornwinder weight functions constructed from semiclassical univariate weights. In this case, it was proved in [7] that w(x, y) satisfies a matrix partial differential equation div(ϕ w(x, y)) = δ w(x, y), but the 2 × 2 matrix ϕ is not symmetric in general, and some of its entries can be rational functions.…”

Three Term Relations for a Class of Bivariate Orthogonal Polynomials

“…Laguerre-Jacobi two variable orthogonal polynomials. Using Agahanov's technique, new examples of bivariate orthogonal polynomials were given in [5].…”

“…Here we study three term relations for Example 1 in [5]. Consider the univariate Laguerre and Jacobi weight functions…”