Nearly identical to the

Taylor Series used in

Calculus, an approximation of a function. Unlike the Taylor Series, which can approximate a function around any number, the Maclaurin Series is specifically for approximating around 0.

The

formula for finding the Maclaurin Series is:

∞ (infinity)
Sigma (E) __f~n(0) x__^{n} where f~n is the n^{th} derivative of f
n=0 x!

Why is the Maclaurin series useful? This simple formula gives us a way to find polynomial approximations of many functions. This can be used to approximate the integral of f, among many other things.