The Laguerre–Sobolev-type orthogonal polynomials

In this paper we study the asymptotic behaviour of polynomials orthogonal with respect to a Sobolev-type inner product 〈p,q〉S=∫0∞p(x)q(x)xαe−xdx+Np(j)(0)q(j)(0), where N∈R+N∈R+ and j∈Nj∈N.We will focus our attention on the outer relative asymptotics with respect to the standard Laguerre polynomials as well as on an analog of the Mehler–Heine formula for the rescaled polynomials.