Noun
radius of convergence (plural radii of convergence)
for a power series
∑
n
=
0
∞
c
n
(
z
−
a
)
n
{\displaystyle \sum _{n=0}^{\infty }c_{n}(z-a)^{n}}
, the unique number
R
=
[
0
,
∞
]
{\displaystyle R=[0,\infty ]}
such that the sum is convergent for
|
z
−
a
|
<
R
{\displaystyle |z-a|
, and divergent for
|
z
−
a
|
>
R
{\displaystyle |z-a|>R}
As a result, the radius of convergence of a Taylor series can be zero. Source: Internet
The radius of convergence is infinite, which implies that : or : Any power series satisfying this criterion will represent an entire function. Source: Internet