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 E （0, 1） ...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 E （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 interval on which these polynomials are orthogonal, Our method is based on the Riemann-Hilbert approach introduced by Delft and Zhou.展开更多
基金Project supported by the the Research Grants Council of the Hong Kong Special Administrative Region,China (No. CityU 102504).
文摘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 E （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 interval on which these polynomials are orthogonal, Our method is based on the Riemann-Hilbert approach introduced by Delft and Zhou.
