Laguerre-Sobolev orthogonal polynomials

In this paper, polynomials that are orthogonal with respect to the inner product (f,g)s=∫+∞0 f(x)g(x)xαe−xdx+λ∫+∞0 f′(x)g′(x)xαe−xdx where α > −1 and λ⩾0, are studied. For these nonstandard orthogonal polynomials algebraic and differential properties as well as the relation with the classical Laguerre polynomials are obtained. Finally, some properties concerning the localization and separation of the zeros of these polynomials are deduced.