Differential operators having Sobolev-type Laguerre polynomials as eigenfunctions: new developments

摘要

In this paper we consider polynomials, orthogonal with respect to an inner product which consists of the classical Laguerre inner product combined with two linear perturbations of Sobolev type at x=0. We derive linear differential operators, of a specific form and usually of infinite order, having these polynomials as eigenfunctions. In the case, α is a nonnegative integer one of the operators is of finite order.