# Definition:Maclaurin Series

## Definition

Let $f$ be a real function which is smooth on the open interval $\openint a b$.

Then the Maclaurin series expansion of $f$ is:

$\displaystyle \sum_{n \mathop = 0}^\infty \frac {x^n} {n!} \map {f^{\paren n} } 0$

It is not necessarily the case that this power series is convergent with sum $\map f x$.

## Source of Name

This entry was named for Colin Maclaurin.