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.References
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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
- 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
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 237-241
- MSC (2000): Primary 33B10; Secondary 11A99
- DOI: https://doi.org/10.1090/S0002-9939-06-08452-8
- MathSciNet review: 2280192