On sobolev orthogonal polynomials with coherent pairs: The Laguerre case, type 1

We study the asymptotic properties of orthogonal polynomials with Sobolev inner product [f, g] = integral(a)(b)f(x)g(x) d mu(x) + lambda integral(a)(b)f' (x)g' (x) d nu(x). The pair {d mu, d nu} is called a coherent pair if there exists nonzero constants D-n such that Q(n)(x) = Pn + 1'(x)/n + 1 + DnPn'(x)/n, n greater than or equal to 1, where P-n(x) and Q(n)(x) are the nth monic orthogonal polynomials with respect to d mu and d nu, 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 the nth root asymptotics and the zero distribution for the Laguerre case, type 1. (C) 1998 Academic Press.