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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Densely algebraic bounds for the exponential function


Author: Seon-Hong Kim
Journal: Proc. Amer. Math. Soc. 135 (2007), 237-241
MSC (2000): Primary 33B10; Secondary 11A99
Published electronically: June 30, 2006
MathSciNet review: 2280192
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Seon-Hong Kim
Affiliation: Department of Mathematics, College of Natural Science, Chosun University, 375 Susuk-dong, Dong-gu, Gwangju, 501-759 Korea
Email: shkim17@mail.chosun.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08452-8
PII: S 0002-9939(06)08452-8
Keywords: Algebraic bounds, exponential function, polynomials
Received by editor(s): January 15, 2005
Received by editor(s) in revised form: July 5, 2005, and August 5, 2005
Published electronically: June 30, 2006
Additional Notes: This study was supported (in part) by research funds from Chosun University, 2004
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2006 American Mathematical Society