Using the steepest descent method for oscillatory Riemann-Hilbert problemsintroduced by Deift and Zhou [Ann. Math. {\bf 137}(1993), 295-368], we deriveasymptotic formulas for the Meixner polynomials in two regions of the complexplane separated by the boundary of a rectangle. The asymptotic formula on theboundary of the rectangle is obtained by taking limits from either inside oroutside. Our results agree with the ones obtained earlier for $z$ on thepositive real line by using the steepest descent method for integrals [Constr.Approx. {\bf 14}(1998), 113-150].
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机译：使用最陡下降法求解由Deift和Zhou提出的振荡Riemann-Hilbert问题。数学。 {\ bf 137}（1993），295-368]，我们推导了复平面的两个区域中被矩形边界分开的Meixner多项式的渐近公式。矩形边界上的渐近公式是通过从内部或外部获取限制来获得的。我们的结果与先前通过使用最速下降法积分的正实线上$ z $所获得的结果一致[Constr.Approx。 {\ bf 14}（1998），113-150]。
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