On Sobolev Orthogonal Polynomials with Coherent Pairs: The Laguerre Case, Type 1

Abstract

We study the asymptotic properties of orthogonal polynomials with Sobolev inner product[formula]The pair }dμ,dν{ is called a coherent pair if there exists nonzero constantsDnsuch that[formula] wherePn(x) andQn(x) are thenth monic orthogonal polynomials with respect todμ anddν, respectively. One can divide the coherent pairs into two cases: the Jacobi case and the Laguerre case. There are two types in each case. We consider thenth root asymptotics and the zero distribution for the Laguerre case, type 1.