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The key objective of this paper is toimprove the approximation of a sufficiently smooth nonperiodic function definedon a compact interval by proposing alternative forms of Fourier seriesexpansions. Unlike in classical Fourier series, the expansion coefficientsherein are explicitly dependent not only on the function itself, but also onits derivatives at the ends of the interval. Each of these series expansionscan be made to converge faster at a desired polynomial rate. These results haveuseful implications to Fourier or harmonic analysis, solutions to differentialequations and boundary value problems, data compression, and so on.

KEYWORDS

Fourier Series, Trigonometric Series, Fourier Approximation, Convergence Acceleration

Cite this paper

Li, W. 2016 Alternative Fourier Series Expansions with Accelerated Convergence. Applied Mathematics, 7, 1824-1845. doi: 10.4236-am.2016.715152.





Author: Wenlong Li

Source: http://www.scirp.org/



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