Asymptotics and zero distribution of Padé polynomials associated with the exponential function (Q1392791)

The asymptotic distribution of zeros and poles of Padé approximants to the exponential function \(e^{-z}\) was extensively studied twenty years ago by Saff, Varga and some other people with help of the saddle point method using to estimate the integrals defining the Padé approximant polynomials. A new approach for locating these zeros and poles is presented in terms of zeros of certain Airy functions used to approximate the integrals representing the Padé approximant polynomials.