a1 School of Mathematics, Informatics and Statistics, Kunsan National University, Kunsan, 573-701, South Korea (email: firstname.lastname@example.org)
In this paper we introduce a set of orthonormal functions, , where n[r] is composed of a sine function and a sigmoidal transformation γr of order r>0. Based on the proposed functions n[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 and then, by reconstructing the existing sigmoidal cosine functions ψn[r] and the presented functions n[r], we develop two kinds of 2-periodic series expansions on . Superiority of the presented sigmoidal-type series in approximating a function by the partial sum is demonstrated by numerical examples.
(Received August 03 2006)
(Revised January 10 2008)
2000 Mathematics subject classification
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