GLOBAL ASYMPTOTICS OF THE HAHN POLYNOMIALS

Global asymptotics of the discrete Chebyshev polynomials

In this paper, we study the asymptotics of the discrete Chebyshev polynomials tn(z,N) as the degree grows to infinity. Global asymptotic formulas are obtained as n → ∞, when the ratio of the parameters n/N = c is a constant in the interval (0, 1). Our method is based on a modified version of the Riemann-Hilbert approach first introduced by Deift and Zhou.

Global asymptotics of the Meixner polynomials

Inner Bounds for the Extreme Zeros of the Hahn, Continuous Hahn and Continuous Dual Hahn Polynomials

We apply Zeilberger’s algorithm to generate relations of finite-type necessary to obtain inner bounds for the extreme zeros of orthogonal polynomial sequences with 3F2 hypergeometric representations. Using this method, we improve previously obtained upper bounds for the smallest and lower bounds for the largest zeros of the Hahn polynomials and we identify inner bounds for the extreme zeros of ...

Constructing bispectral dual Hahn polynomials

Using the concept ofD-operator and the classical discrete family of dual Hahn, we construct orthogonal polynomials (qn)n which are also eigenfunctions of higher order difference operators. c ⃝ 2014 Elsevier Inc. All rights reserved. MSC: 33C45; 33E30; 42C05

Global Asymptotics of Krawtchouk Polynomials – a Riemann-Hilbert Approach

In this paper, we study the asymptotics of the Krawtchouk polynomials KN n (z; p, q) as the degree n becomes large. Asymptotic expansions are obtained when the ratio of the parameters n/N tends to a limit c ∈ (0, 1) as n →∞. The results are globally valid in one or two regions in the complex z-plane depending on the values of c and p; in particular, they are valid in regions containing the inte...