TY - JOUR T1 - On Coefficient Polynomials of Cubic Hermite-Padé Approximations to the Exponential Function JO - Journal of Computational Mathematics VL - 4 SP - 383 EP - 392 PY - 2005 DA - 2005/08 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8824.html KW - Padé-type approximant, Cubic Hermite-Padé approximation, Hypergeometric function, Saddle point method. AB -
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.