Some Asymptotic Properties of Pade 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, Pade approximants to 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. 1. Introduction. There is considerable interest in properties of Pade approximants to the exponential, not least because of their application in methods for solving those systems of ordinary differential equations which arise in mathematical models of physical processes. In this paper, some asymptotic properties of Pade approximants to e-x are found by using the method of matched asymptotic expansions. First, we analyze the behavior of the real zero of odd-degree denominators along any straight line path through the Pade table; second, a result due to Saff, Varga and Ni (6) concerning the error in the uniform norm on (0, oo) incurred by these approximants is reconsidered.