By definition, the Taylor series of $f(x)$ about the expansion center $x = a$ is:
$f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \dots = \sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!}(x - a)^n$
When $a = 0$, this formula reduces to the Maclaurin series.