\begin{definition}[Definition:Fourier Series/Fourier Coefficient/Range 2 Pi]
Let $f: \R \to \R$ be a function such that $\ds \int_\alpha^{\alpha + 2 \pi} \map f x \rd x$ converges absolutely.
Let:
:$\ds \frac {a_0} 2 + \sum_{n \mathop = 1}^\infty \paren {a_n \cos n x + b_n \sin n x}$
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 $f$.
{{NamedforDef|Joseph Fourier|cat = Fourier}}
\end{definition}