On higher order ladder operators for classical orthogonal polynomials

Abstract

We analyze the algebraic structure of higher order ladder operators for classical orthogonal polynomials (Hermite, Laguerre, Jacobi, Bessel) in terms of their moment functionals and two first order ladder operators, $J_n^+$ and $J_n^-$. We study operational expressions for these ladder operators in terms of certain integro-differential operators.