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