On Coefficient Polynomials of Cubic Hermite-Padé Approximations to the Exponential Function

Authors

  • Cheng-De Zheng, Guo-Can Wang & Zhi-Bin Li

Keywords:

Padé-type approximant, Cubic Hermite-Padé approximation, Hypergeometric function, Saddle point method.

Abstract

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.  

Published

2005-08-02

Issue

Section

Articles