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

AbstractThis paper analyzes polynomials orthogonal with respect to the Sobolev inner product ϕ̃(f,g)=∫Rf(x)g(x)ϱ(x)dx+λ−1f(r)(c)g(r)(c)withλ∈R+, c∈R, 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