Journal of approximation theory vol:129 issue:2 pages:129-166
We describe methods for the derivation of strong asymptotics for the denominator polynomials and the remainder of Pade approximants for a Markov function with a complex and varying weight. Two approaches, both based on a Riemann-Hilbert problem, are presented. The first method uses a scalar Riemann-Hilbert boundary value problem on a two-sheeted Riemann surface, the second approach uses a matrix Riemann-Hilbert problem. The result for a varying weight is not with the most general conditions possible, but the loss of generality is compensated by an easier and transparent proof. (C) 2004 Elsevier Inc. All rights reserved.