Definition:Fourier Series/Fourier Coefficient

Definition
Let $f: \R \to \R$ be a function such that $\displaystyle \int_\alpha^{\alpha + 2 l} f \left({x}\right) \, \mathrm d x$ converges absolutely.

Let:
 * $\displaystyle \frac {a_0} 2 + \sum_{n \mathop = 1}^\infty \left({a_n \cos \frac {n \pi x} l + b_n \sin \frac {n \pi x} l}\right)$

be the Fourier series for $f$.

The constants:
 * $a_0, a_1, a_2, \ldots, a_n, \ldots; b_1, b_2, \ldots, b_n, \ldots$

are the Fourier coefficients of $f$.