Krawtchouk多项式零点的渐近展开及其误差限

Asymptotic Expansions of Zeros for Krawtchouk Polynomials With Error Bounds

Krawtchouk多项式在现代物理学中有着广泛应用·基于Li和Wong的结果,利用Airy函数改进了Krawtchouk多项式的渐近展开式,而且得到了一个一致有效的渐近展开式·进一步,利用Airy函数零点的性质,推导出了Krawtchouk多项式零点的渐近展开式,并讨论了其相应的误差限·同时还给出了Krawtchouk多项式和其零点的渐近性态,它优于Li和Wong的结果·

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