This paper analyzes polynomials orthogonal with respect to the Sobolev inner product with and ϱ(x)is a weight function.
We study this family of orthogonal polynomials, as linked to the polynomials orthogonal with respect to ϱ(x) and we find the recurrence relation verified by such a family. If the weight ϱ is semiclassical we obtain a second order differential equation for these polynomials. Finally, an illustrative example is shown.