Some asymptotic properties of Padé approximants to 𝑒^{-𝑥}

Abstract

The method of matched asymptotic expansions is used to analyze the asymptotic behavior of the real zeros of, and error incurred by, Padé approximants to e − x {e^{ - x}} . These approximants are of interest because of their application in solving systems of ordinary differential equations arising from mathematical models of physical processes, for example, the heat equation.