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

Underhill, C.

doi:10.1090/S0025-5718-1986-0842133-2

Some asymptotic properties of Padé approximants to $e^ {-x}$
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Math. Comp. 47 (1986), 253-263 Request permission

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 ${e^{ - x}}$. 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.

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