Definition 8.4.3: Taylor Series

Suppose f is an infinitely often differentiable function on a set D and c D. Then the series

T_f(x, c) =

is called the (formal) Taylor series of f centered at, or around, c. If c = 0 the series is sometimes also called MacLaurin Series, i.e. a MacLaurin series is a Taylor series around zero.

Context