Year: 2005
Journal of Computational Mathematics, Vol. 23 (2005), Iss. 4 : pp. 383–392
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2005-JCM-8824
Journal of Computational Mathematics, Vol. 23 (2005), Iss. 4 : pp. 383–392
Published online: 2005-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Padé-type approximant Cubic Hermite-Padé approximation Hypergeometric function Saddle point method.