ON COEFFICIENT POLYNOMIALS OF CUBIC HERMITE-PADé APPROXIMATIONS TO THE EXPONENTIAL FUNCTION  

作　　者：Cheng-de Zheng Guo-can Wang Zhi-bin Li 

机构地区：[1]Department of Mathematical Physics, Dalian Jiaotong University, Dalian 116028, China

出　　处：《Journal of Computational Mathematics》2005年第4期383-392,共10页计算数学（英文）

摘　　要：The polynomials related with cubic Hermite-Padé approximation to the exponential function are investigated which have degrees at most n, m, s respectively. A connection is given between the coefficients of each of the polynomials and certain hypergeometric functions, which leads to a simple expression for a polynomial in a special case. Contour integral representations of the polynomials are given. By using of the saddle point method the exact asymptotics of the polynomials are derived as n, m, s tend to infinity through certain ray sequence. Some further uniform asymptotic aspects of the polynomials are also discussed.The polynomials related with cubic Hermite-Padé approximation to the exponential function are investigated which have degrees at most n, m, s respectively. A connection is given between the coefficients of each of the polynomials and certain hypergeometric functions, which leads to a simple expression for a polynomial in a special case. Contour integral representations of the polynomials are given. By using of the saddle point method the exact asymptotics of the polynomials are derived as n, m, s tend to infinity through certain ray sequence. Some further uniform asymptotic aspects of the polynomials are also discussed.

关 键 词：Padé-type approximant Cubic Hermite-Padé approximation Hypergeometric function Saddle point method 

分 类 号：O18[理学—数学]