Inner products involving differences: The Meixner-Sobolev polynomials

In this paper, polynomials which are orthogonal with respect to the inner p roduct [p, q](S) = Sigma(s=0)(infinity)p(s)q(s) (mu(s)Gamma(gamma + s))/(Gamma(s 1)Gamma(gamma)) + lambda Sigma(s=0)(infinity)Delta p(s)Delta q(s) (mu(s)Ga mma(gamma + s))/(Gamma(s + 1)Gamma(gamma)), where 0 < mu < 1, gamma > 0 and lambda greater than or equal to 0 are studi ed. For these polynomials, algebraic properties and difference equations ar e obtained as well as their relation with the Meixner polynomials. Moreover , some properties about the zeros of these polynomials are deduced.