Orthogonal Polynomials Satisfying Higher Order Differential Equations

Abstract

There are various possible iterative schemes available to produce differential equations of any even order. Multiples of the second order operators, fourth order operators and sixth order operators will generate a host of examples [10], but these “do not count” in a sense. Indeed their spectral resolutions all look like

$$A = \int {{{\lambda }^{n}}dE(\lambda )}$$

where n > 1, and E(λ) is the spectral measure for the lowest order operator.