From: tim274@aol.com (Tim274)
Newsgroups: sci.math
Subject: Re: Convergence of Pade Approximations
Date: 6 Nov 1997 17:04:19 GMT

>Does anyone *know* (not just believe) or have a reference whether or under
>what 
>circumstances Pade approximations do converge if the degree of the
>polynomials 
>in the numerator and the denominator tend to infinity? The particular
>question 
>I'm interested in is whether
>
>            P_n,n(x)
>        lim --------  = e^x      as n -> infinity
>            Q_n,n(x)
>
>for all real x. Here P_n,n(x) and Q_n,n(x) are the numerator/denominator 
>polynomials of the Pade approximation for e^x.
>
>I would appreciate any help...
>
>	Florian
>
>--------------
>Florian Herzig
>fh210@cam.ac.uk

The answer is yes. Try a set of papers by Richard Varga and Ed Saff in the
 1970's, called "Zeros and Poles of Pade Approximants to e^z, I, II and III".

Tim Norfolk