Fourier Coefficients

Odd Sine Series

$$B\_n=\frac{1}{L}\int \_{-L}^{L}f(x)\sin \left(\frac{n\pi x}{L}\right),=\frac{2}{L}\int \_0^L\sin \left(\frac{n\pi x}{L}\right),dx$$

Even Cosine Series

$$A\_0=\frac{1}{2L}\int \_{-L}^{L}f(x),dx$$ $$A\_n=\frac{1}{L}\int \_{-L}^{L}f(x)\sin \left(\frac{n\pi x}{L}\right),dx$$