On a class of polynomials orthogonal with respect to a discrete Sobolev inner product

This paper analyzes polynomials orthogonal with respect to the Sobolev inner product @(Lg) = I f(x)g(x)e(x)dx+~-‘f”‘(c)g”‘(c) iF with I E IR+, c E [R, and p(x) is a weight function. We study this family of orthogonal polynomials, as linked to the polynomials orthogonal with respect to Q(X) and we find the recurrence relation verified by such a family. If the weight Q is semiclassical we obtain a second order differential equation for these polynomials. Finally, an illustrative example is shown.