Rational approximation of exponential function

From: Vinay Kariwala (kariwala_at_ualberta.ca)
Date: 06/11/04 

Date: Fri, 11 Jun 2004 23:33:31 +0000 (UTC)

Dear all,

This problem would be trivial for most of you. I am looking for an
approximation of the exponential function, e^(-x) with the following properties:

1. The nth order approximation f(x,n) should be rational, i.e. it
should be possible to write f(x,n) as ratio of polynomials in x. f
(x,n) = g(x,n)/h(x,n), where g(x,n) has less number of zeros than h(x,n).

2. As n approaches infinity, f(x,n) should converge back to the
exponential function.

Any comments or suggestions will be very helpful.

Thanks

Vinay

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