We consider asymptotics of orthogonal polynomials with respect to weights w
(x)dx = e(-Q(x))dx on the real line, where Q(x) = Sigma(k=0)(2m) q(k)x(k),
q(2m) > 0, denotes a polynomial of even order with positive leading coeffic
ient. The orthogonal polynomial problem is formulated as a Riemann-Hilbert
problem following [22, 23].
We employ the steepest-descent-type method introduced in [18] and further d
eveloped in [17, 19] in order to obtain uniform Plancherel-Rotach-type asym
ptotics in the entire complex plane, as well as asymptotic formulae for the
zeros, the leading coefficients, and the recurrence coefficients of the or
thogonal polynomials. (C) 1999 John Wiley & Sons, Inc.