Fourier Series
Tags: #math #fourier seriesEquation
$$y(x)=c_{0}+\sum^{M}_{m=1}c_{m}\cos mx+\sum^{M^{'}}_{m=1}s_{m}\sin mx \\ c_{0}=\frac{1}{2\pi}\int^{\pi}_{-\pi}y(x) \mathrm{d} x \\ c_{m}=\frac{1}{\pi}\int^{\pi}_{-\pi}y(x) \cos mx \mathrm{d} x \\ s_{m}=\frac{1}{\pi}\int^{\pi}_{-\pi}y(x) \sin mx \mathrm{d} x$$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
If y(x) is a function defined in the range then the above fourier series expansion formula holds.
- Fourier series for ranges t belongs to [0,T]
- Fourier series for ranges x belongs to [0,L]
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