An algebraic approach to certain differential eigenvalue problems Original Research Article

It has been known for a long time that the solutions of certain differential equation systems are orthogonal polynomials. Some of the properties of these orthogonal polynomials are traditionally derived from the differential equations. In this note a number of properties are derived just from the recurrence relation of the orthogonal polynomial. In particular we reestablish some recent results by Kwon and Littlejohn on the Laguerre polynomials {L(−k)n(x)}, k > 0, where the orthogonality is with respect to a weighted Sobolev inner product.