Asymptotic behavior of the partial derivatives of Laguerre kernels and some applications

Abstract

Orthogonal polynomials Laguerre polynomials Asymptotics Diagonal Christoffel-Darboux kernels Sobolev-type orthogonal polynomialsThe aim of this paper is to present some new results about the asymptotic behavior of the partial derivatives of the kernel polynomials associated with the Gamma distribution. We also show how these results can be used in order to obtain the inner relative asymptotics for certain Laguerre-Sobolev type polynomials.