  In this contribution we deal with a varying discrete Sobolev inner product
involving the Jacobi weight. Our aim is to study the asymptotic properties of
the corresponding orthogonal polynomials and the behavior of their zeros. We
are interested in Mehler-Heine type formulae because they describe the
essential differences from the point of view of the asymptotic behavior between
these Sobolev orthogonal polynomials and the Jacobi ones. Moreover, this
asymptotic behavior provides an approximation of the zeros of the Sobolev
polynomials in terms of the zeros of other well-known special functions. We
generalize some results appeared in the literature very recently.
