Strong asymptotics of polynomials orthogonal with respect to a complex weight

For polynomials orthogonal with respect to a complex-valued weight on the closed interval $\Delta=[-1,1]$ a strong asymptotic formula in a neighbourhood of $\Delta$ is obtained. In particular, for the ‘trigonometric’ weight $\rho_0(x)=e^{ix}$, $x\in\Delta$, this formula yields a description of the asymptotic behaviour of each of the $n$ zeros of the $n$th orthogonal polynomial as $n\to\infty$. This strong asymptotic formula is deduced on the basis of Nuttall's singular integral equation.
Bibliography: 28 titles.