Maclaurin Series Definition

Any Taylor series that is centred at 0 (i.e., for which the origin is the reference point used to derive the series from its associated function); for a given infinitely differentiable complex function \textstyle f, the power series \textstyle f(0)+\frac {f'(0)}{1!}x+ \frac{f(0)}{2!}x^2+ \frac{f(0)}{3!}x^3+ \cdots = \sum_{n=0}^{\infty} \frac{f^{(n)}(0)}{n!} \, x^{n}.