Fourier sine and cosine series

In mathematics, particularly the field of calculus and Fourier analysis, the Fourier sine and cosine series are two mathematical series named after Joseph Fourier.

Sine series

The Fourier sine series is given by

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Where

$c_{n}={\frac {2}{L}}\int _{0}^{L}f(x)\sin {\frac {n\pi x}{L}}\,dx$

Where $L$ is some integer value, $f(x)$ is the function of x to be transformed, and $n$ is some arbitrary integer.

Cosine series

The Fourier cosine series is given by

$c_{n}={\frac {2}{L}}\int _{0}^{L}f(x)\cos {\frac {n\pi x}{L}}\,dx$

See also

• Fourier series

• Fourier analysis