ON COEFFICIENT POLYNOMIALS OF CUBIC HERMITE-PADE APPROXIMATIONS TO THE EXPONENTIAL FUNCTION

摘要

The polynomials related with cubic Hermite-Pade 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.