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

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.