Asymptotics of Sobolev orthogonal polynomials for coherent pairs of Jacobi type

Let {S-n}(n) denote a sequence of polynomials orthogonal with respect to the Sobolev inner product (f,g)s = integral f(x)g(x) d psi(0)(x) + lambda integral f'(x)g'(x) d psi(1)(x) where lambda > 0 and (d psi(0), d psi(1)) is a so-called coherent pair with at least one of the measures d psi(0) or d psi(1) a Jacobi measure. We investigate the asymptotic behaviour of S-n(x), for n --> +infinity and x fixed, x is an element of C \ [ - 1, 1] as well as x is an element of (-1, 1). (C) 1999 Elsevier Science B.V. All rights reserved. MSG: 33 C 45.