\begin{definition}[Definition:Maclaurin Series]
Let $f$ be a real function which is smooth on the open interval $\openint a b$.
Then the '''Maclaurin series expansion of $f$''' is:
:$\ds \sum_{n \mathop = 0}^\infty \frac {x^n} {n!} \map {f^{\paren n} } 0$
It is ''not'' necessarily the case that this power series is convergent with sum $\map f x$.
{{NamedforDef|Colin Maclaurin|cat = Maclaurin}}
\end{definition}