Volume 23, Issue 4
On Coefficient Polynomials of Cubic Hermite-Pad\'E Approximations to the Exponential Function

Cheng-De Zheng, Guo-Can Wang & Zhi-Bin Li

DOI:

J. Comp. Math., 23 (2005), pp. 383-392

Published online: 2005-08

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  • Abstract

The polynomials related with cubic Hermite-Pad\'e 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.

  • Keywords

Pad\'{e}-type approximant Cubic Hermite-Pad\'e approximation Hypergeometric function Saddle point method

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@Article{JCM-23-383, author = {}, title = {On Coefficient Polynomials of Cubic Hermite-Pad\'E Approximations to the Exponential Function}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {4}, pages = {383--392}, abstract = { The polynomials related with cubic Hermite-Pad\'e 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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8824.html} }
TY - JOUR T1 - On Coefficient Polynomials of Cubic Hermite-Pad\'E 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://dor.org/ UR - https://global-sci.org/intro/article_detail/jcm/8824.html KW - Pad\'{e}-type approximant KW - Cubic Hermite-Pad\'e approximation KW - Hypergeometric function KW - Saddle point method AB - The polynomials related with cubic Hermite-Pad\'e 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.
Cheng-De Zheng, Guo-Can Wang & Zhi-Bin Li. (1970). On Coefficient Polynomials of Cubic Hermite-Pad\'E Approximations to the Exponential Function. Journal of Computational Mathematics. 23 (4). 383-392. doi:
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