Zero asymptotics of Laurent orthogonal polynomials

Let {h(kappa)(z)} be the sequence of polynomials satisfying integral(0)(+x) h(m)(x) h(n)(x) N(-lambda n)rho(x) = delta(mm), 0 less than or equal to m less than or equal to n, where lambda(n) is an element of [0, 2n], n is an element of N. For a wide class of weights d rho(x) and under the assumption lim(n-->alpha) lambda(n)/(2n) = 0 is an element of [0, 1], two descriptions of the zero asymptotics of {h(n)(z)} are obtained. Furthermore, their analogues for polynomials orthogonal on [-1, 1] with respect to varying weights are considered. These results continue the study begun in [3]. (C) 1996 Academic Press, Inc.