Orthogonal polynomials on systems of non-uniform lattices from compatibility conditions

Abstract

We deduce difference equations in the matrix form for Laguerre–Hahn orthogonal polynomials on systems of non-uniform lattices, the so-called compatibility conditions, involving the transfer matrices. As a consequence, we obtain closed form expressions for the recurrence relation coefficients of the Laguerre–Hahn polynomials of class zero.