For a bilinear form obtained by adding a Dirac mass to a positive definite moment functional in several variables, explicit formulas of orthogonal polynomials are derived from the orthogonal polynomials associated with the moment functional. Explicit
formula for the reproducing kernel is also derived and used to establish certain inequalities for classical orthogonal polynomials.
In this paper we deal with a family of non--standard polynomials orthogonal with respect to an inner product involving differences. This type of inner product is the so--called $Delta$--Sobolev inner product. Concretely, we consider the case in which
both measures appearing in the inner product correspond to the Pascal distribution (the orthogonal polynomials associated to this distribution are known as Meixner polynomials). The aim of this work is to obtain a generating function for the $Delta$--Meixner--Sobolev orthogonal polynomials and, by using a limit process, recover a generating function for Laguerre--Sobolev orthogonal polynomials.
