Fourier series : Examples of Fourier series development

Examples of Fourier series development
Fourier series

Author : Hervé QUEFFÉLEC

Publication date: January 10, 1999 | Lire en français

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3. Examples of Fourier series development

Proposition 3

Let f ∊ L¹ , a_n = a_n (f ) , b_n = b_n (f ) , c_n = c_n (f ).

a)If fis even, we have b_n = 0

and : $S_{N} (f, x) = \frac{a_{0}}{2} + \sum_{1}^{N} a_{n} \cos nx = c_{0} + 2$

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Ongoing reading
Examples of Fourier series development

(1) - DAVIS (P.) - Interpolation and approximation.
(2) - KUIPERS (L.), NIEDERREITER (H.) - Uniform distribution of sequences. - Wiley-Interscience Series, 1974.
(3) - ZYGMUND (A.) - Trigonometric Series, - Second Edition. Cambridge University Press, 1959.

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