1.NounAny smooth (infinitely differentiable) function
f
{\displaystyle f}
, defined on an open set
D
⊆
C
(
or
⊆
R
)
{\displaystyle D\subseteq \mathbb {C} \ ({\textit {or}}\subseteq \mathbb {R} )}
, whose value in some neighbourhood of any given point
x
0
∈
D
{\displaystyle x_{0}\in D}
is given by the Taylor series
∑
n
=
0
∞
f
(
n
)
(
x
0
)
n
!
(
x
−
x
0
)
n
{\displaystyle \textstyle \sum _{n=0}^{\infty }{\frac {f^{(n)}(x_{0})}{n!}}(x-x_{0})^{n}}
.