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Bull. Korean Math. Soc. 2004; 41(1): 27-43

Printed March 1, 2004

Copyright © The Korean Mathematical Society.

Analytic properties of the limits of the even and odd hyperpower sequences

Yunhi Cho and Young-One Kim

University of Seoul, Seoul National University

Abstract

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Let $h_e(x)$ and $h_o(x)$ denote the limits of the sequences $\{{}^{2n}x\}$ and $\{{}^{2n+1}x\}$, respectively. Asymptotic formulas for the functions $h_e$ and $h_o$ at the points $e^{-e}$ and $0$ are established.

Keywords: approximation, asymptotic formula, hyperpower sequence

MSC numbers: 26A06, 26A18, 26A24

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