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16.8: Fourier Series

  • Page ID
    107067
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    For a periodic function of period \(2L\):

    \[\begin{array}{c} f(x)=\frac{a_0}{2}+\sum\limits_{n=1}^{\infty}a_n\cos\left ( \frac{n \pi x}{L} \right )+\sum\limits_{n=1}^{\infty}b_n\sin\left ( \frac{n \pi x}{L} \right ) \\ a_0=\frac{1}{L}\int\limits_{-L}^{L}f(x)dx \\ a_n=\frac{1}{L}\int\limits_{-L}^{L}f(x)\cos{\left(\frac{n \pi x}{L} \right)}dx \\ b_n=\frac{1}{L}\int\limits_{-L}^{L}f(x)\sin{\left(\frac{n \pi x}{L} \right)}dx \end{array} \nonumber\]


    This page titled 16.8: Fourier Series is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Marcia Levitus via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.