Definition:Fourier Series/Fourier Coefficient/Range 2 Pi

Definition
Let $f: \R \to \R$ be a function such that $\displaystyle \int_\alpha^{\alpha + 2 \pi} \map f x \rd x$ converges absolutely.

Let:
 * $\displaystyle \frac {a_0} 2 + \sum_{n \mathop = 1}^\infty \paren {a_n \cos n x + b_n \sin n x}$

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 $f$.