Densely algebraic bounds for the exponential function

Kim, Seon-Hong

doi:10.1090/S0002-9939-06-08452-8

Densely algebraic bounds for the exponential function
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by Seon-Hong Kim PDF

Proc. Amer. Math. Soc. 135 (2007), 237-241 Request permission

Abstract:

An upper bound for $e^{x}$ that implies the inequality between the arithmetic and geometric means is generalized with the introduction of a new parameter $n$. The new upper bound is smoothly and densely algebraic in $n$, and valid for $-b<x<1$ for arbitrarily large positive $b$ provided that $n$ ($>1$) is sufficiently close to $1$. The range of its validity for negative $x$ is investigated through the study of a certain family of quadrinomials.

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