# Maclaurin Series Formula

A Maclaurin series is a function that has expansion series that gives the sum of derivatives of that function. The Maclaurin series of a function $f(x)$ up to order n may be found using Series $[f, {x, 0, n}]$.

It is a special case of Taylor series when x = 0. The Maclaurin series is given by

$\large f(x)=f(x_{0})+{f}'(x_{0})(x-x_{0})+\frac{{f}”(x_{0})}{2!}(x-x_{0})^{2}+\frac{{f}”'(x_{0})}{3!}(x-x_{0})^{3}+…..$

The Maclaurin series formula is

$\large f(x)=\sum_{n=0}^{\infty}\frac{f^{n}(x_{0})}{n!}(x-x_{0})$

Where,
f(xo), f’(xo), f’‘(xo)……. are the successive differentials when xo = 0.