\begin{definition}[Definition:Fourier Series/Fourier Coefficient]
Let $\alpha \in \R$ be a real number.
Let $\lambda \in \R_{>0}$ be a strictly positive real number.
Let $f: \R \to \R$ be a function such that $\ds \int_\alpha^{\alpha + 2 \lambda} \map f x \rd x$ converges absolutely.
Let:
:$\ds \frac {a_0} 2 + \sum_{n \mathop = 1}^\infty \paren {a_n \cos \frac {n \pi x} \lambda + b_n \sin \frac {n \pi x} \lambda}$
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}}
\end{definition}