@Article{JCM-23-383, author = {}, title = {On Coefficient Polynomials of Cubic Hermite-Padé 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-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.
}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8824.html} }