Abstract: Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds are discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.

Key words: Krawtchouk polynomial, asymptotic expansion, zero, error bounds