Difference equations for some orthogonal polynomials

Differential and Difference Equations for Products of Classical Orthogonal Polynomials

Difference equations for discrete classical multiple orthogonal polynomials

For discrete multiple orthogonal polynomials such as the multiple Charlier polynomials, the multiple Meixner polynomials, and the multiple Hahn polynomials, we first find a lowering operator and then give a (r + 1)th order difference equation by combining the lowering operator with the raising operator. As a corollary, explicit third order difference equations for discrete multiple orthogonal p...

Orthogonal matrix polynomials satisfying second order difference equations

We develop a method that allows us to construct families of orthogonal matrix polynomials of size N ×N satisfying second order difference equations with polynomial coefficients. The existence (and properties) of these orthogonal families strongly depends on the non commutativity of the matrix product, the existence of singular matrices and the matrix size N .

Discrete Orthogonal Polynomials and Difference Equations of Several Variables

The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem.

On Factorization and Solutions of q-difference Equations Satisfied by some Classes of Orthogonal Polynomials

Equations Satisfied by some Classes of Orthogonal Polynomials M. FOUPOUAGNIGNI*, W. KOEPF and A. RONVEAUX University of Yaounde I, Advanced School of Education, Department of Mathematics. P.O. Box 47 Yaounde, Cameroon; University of Kassel, Department of Mathematics and Computer Science, Heinrich-Plett Str. 40, 34132 Kassel, Germany; Facultés Universitaires Notre Dame de la Paix, B-5000 Namur, ...