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• W2012134051 abstract "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." @default.
• W2012134051 created "2016-06-24" @default.
• W2012134051 creator A5075681448 @default.
• W2012134051 date "2008-01-01" @default.
• W2012134051 modified "2023-10-16" @default.
• W2012134051 title "SIGMOIDAL-TYPE SERIES EXPANSION" @default.
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• W2012134051 doi "https://doi.org/10.1017/s1446181108000060" @default.
• W2012134051 hasPublicationYear "2008" @default.
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