Fourier Series Equation Formula Latex Code and Summary

Fourier Series

Tags: #math #fourier series

Equation

$$y(x)=c_{0}+\sum^{M}_{m=1}c_{m}\cos mx+\sum^{M^{'}}_{m=1}s_{m}\sin mx \\ c_{0}=\frac{1}{2\pi}\int^{\pi}_{-\pi}y(x) \mathrm{d} x \\ c_{m}=\frac{1}{\pi}\int^{\pi}_{-\pi}y(x) \cos mx \mathrm{d} x \\ s_{m}=\frac{1}{\pi}\int^{\pi}_{-\pi}y(x) \sin mx \mathrm{d} x$$

Latex Code

                                 y(x)=c_{0}+\sum^{M}_{m=1}c_{m}\cos mx+\sum^{M^{'}}_{m=1}s_{m}\sin mx \\
c_{0}=\frac{1}{2\pi}\int^{\pi}_{-\pi}y(x) \mathrm{d} x \\
c_{m}=\frac{1}{\pi}\int^{\pi}_{-\pi}y(x) \cos mx \mathrm{d} x \\
s_{m}=\frac{1}{\pi}\int^{\pi}_{-\pi}y(x) \sin mx \mathrm{d} x

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Introduction

$y(x)=c_{0}+\sum^{M}_{m=1}c_{m}\cos mx+\sum^{M^{'}}_{m=1}s_{m}\sin mx \\ c_{0}=\frac{1}{2\pi}\int^{\pi}_{-\pi}y(x) \mathrm{d} x \\ c_{m}=\frac{1}{\pi}\int^{\pi}_{-\pi}y(x) \cos mx \mathrm{d} x \\ s_{m}=\frac{1}{\pi}\int^{\pi}_{-\pi}y(x) \sin mx \mathrm{d} x$

If y(x) is a function defined in the range $x \in [-\pi,\pi]$ then the above fourier series expansion formula holds.

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Patricia Johnson

My one wish right now is to pass this test.

2024-04-19 00:00
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Samuel Evans reply to Patricia Johnson

Nice~

2024-05-18 00:00:00.0
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Joseph Davis

It's my earnest desire to pass this exam.

2024-03-24 00:00
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You can make it...

2024-03-30 00:00:00.0
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Noel Bowers

I really want to ace this exam.

2023-10-30 00:00
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Matthew Taylor reply to Noel Bowers

Nice~

2023-11-02 00:00:00.0
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