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arXiv · 1101.4370

Global Asymptotics of the Meixner Polynomials

X. -S. Wang·R. Wong
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Abstract

Using the steepest descent method for oscillatory Riemann-Hilbert problems introduced by Deift and Zhou [Ann. Math. {\bf 137}(1993), 295-368], we derive asymptotic formulas for the Meixner polynomials in two regions of the complex plane separated by the boundary of a rectangle. The asymptotic formula on the boundary of the rectangle is obtained by taking limits from either inside or outside. Our results agree with the ones obtained earlier for $z$ on the positive real line by using the steepest descent method for integrals [Constr. Approx. {\bf 14}(1998), 113-150].

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X. -S. Wang, R. Wong. 2011-01-23. Global Asymptotics of the Meixner Polynomials. https://arxiv.org/abs/1101.4370

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