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SIGMOIDAL-TYPE SERIES EXPANSION

Part of: Approximations and expansions

Published online by Cambridge University Press:  01 January 2008

BEONG IN YUN
BEONG IN YUN*
Affiliation:
School of Mathematics, Informatics and Statistics, Kunsan National University, Kunsan, 573-701, South Korea (email: biyun@kunsan.ac.kr)
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Abstract

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In this paper we introduce a set of orthonormal functions, , where ϕn[r] is composed of a sine function and a sigmoidal transformation γr of order r>0. Based on the proposed functions ϕn[r] named by sigmoidal sine functions, we consider a series expansion of a function on the interval [−1,1] and the related convergence analysis. Furthermore, we extend the sigmoidal transformation to the whole real line ℝ and then, by reconstructing the existing sigmoidal cosine functions ψn[r] and the presented functions ϕn[r], we develop two kinds of 2-periodic series expansions on ℝ. Superiority of the presented sigmoidal-type series in approximating a function by the partial sum is demonstrated by numerical examples.

Keywords

Fourier seriessigmoidal transformationsigmoidal series

MSC classification

Secondary: 41A58: Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 3 , January 2008 , pp. 431 - 450
Copyright
Copyright © Australian Mathematical Society 2008

References

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