TY - JOUR
T1 - On Coefficient Polynomials of Cubic Hermite-Padé Approximations to the Exponential Function
AU - Cheng-De Zheng, Guo-Can Wang & Zhi-Bin Li
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 - <p style="text-align: justify;">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. &nbsp;</p>