Maclaurin Series
The Maclaurin Series is a special case of the Taylor Series, which represents a function as an infinite sum of terms calculated from the function's derivatives at a single point. Specifically, the Maclaurin Series expands a function around the point zero. It provides a way to approximate complex functions using polynomials, making calculations simpler.
The general formula for the Maclaurin Series of a function f(x) is given by f(x) = f(0) + f'(0)x + \fracf''(0)2!x^2 + \fracf'''(0)3!x^3 + \ldots . This series is particularly useful in calculus and mathematical analysis for approximating functions near the origin.