The polynomials related with cubic Hermite-PadÃ© 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} }