Definition:Maclaurin Series

Definition
Let $f$ be a real function which is smooth on the open interval $\left({a \,.\,.\, b}\right)$.

Then the Maclaurin series expansion of $f$ is:
 * $\displaystyle \sum_{n \mathop = 0}^\infty \frac {x^n} {n!} f^{\left({n}\right)} \left({0}\right)$

It is not necessarily the case that this power series is convergent with sum $f \left({x}\right)$.