Orthogonal polynomials satisfying fourth order differential equations

Abstract

SynopsisThese polynomials, which are intimately connected with the Legendre, Laguerre and Jacobi polynomials, are orthogonal with respect to Stieltjes weight functions which are absolutely continuous on (− 1, 1), (0, ∞) and (0, 1), respectively, but which have jumps at some of the intervals' ends. Each set satisfies a fourth order differential equation of the form Ly = λny, where the coefficients of the operator L depends only upon the independent variable. The polynomials also have other properties, which are usually associated with the classical orthogonal polynomials.