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Krawtchouk多项式零点的渐近展开及其误差限

 引用本文: 朱晓峰, 李秀淳. Krawtchouk多项式零点的渐近展开及其误差限[J]. 应用数学和力学, 2006, 27(12): 1424-1430.
ZHU Xiao-feng, LI Xiu-chun. Asymptotic Expansions of Zeros for Krawtchouk Polynomials With Error Bounds[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1424-1430.
 Citation: ZHU Xiao-feng, LI Xiu-chun. Asymptotic Expansions of Zeros for Krawtchouk Polynomials With Error Bounds[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1424-1430.

• 中图分类号: O174

Asymptotic Expansions of Zeros for Krawtchouk Polynomials With Error Bounds

• 摘要: 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A·D2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．
•  [1] Sharapudinov I I. Asymptotic properties of Krawtchouk polynomials[J].Mat Zametki，1988,44(5):682—693;English translation,Math Notes,1988,44(5):855—862. [2] Ismail M E H, Simeonov P. Strong asymptotics for Krawtchouk polynomials[J].J Comput Appl Math，1998,100(2):121—144. [3] Li X C, Wong R. A uniform asymptotic expansion for Krawtchouk polynomials[J].Journal of Approximation Theory,2000,106(1):155—184. [4] Olver F W J.Uniform asymptotic expansions for Weber parabolic cylinder functions of large order[J].J Res Nat Bur Standards Sect B,1959,63(2):131—169. [5] Hethcote H W. Error bounds for asymptotic approximations of zeros of transcendental functions[J].SIAM J Math Anal,1970,1(2):147—152. doi: 10.1137/0501015 [6] Ma E J,Zhu X F，Li X C. Asymptotic approximations of Jacobi polynomials and their zeros with error bounds[J].Tsinghua Science and Technology,2003,8(1):71—78. [7] 朱晓峰，李秀淳.关于Jacobi函数渐近性态[J]. 数学的实践与认识，2005，35(4):200—205. [8] Zhu X F, Li X C.Asymptotic approximations of Jacobi polynomials and their zeros with error bounds[J].Acta Mathematica Sinica,2006,22(3):729—740.
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出版历程
• 收稿日期:  2005-03-10
• 修回日期:  2006-04-17
• 刊出日期:  2006-12-15

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