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) xn where f~n is the nth 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.