Abel sum
Noun
Meaning
Abel sum (plural Abel sums)
(mathematical analysis) Given a power series
f
(
x
)
=
∑
n
=
0
∞
a
n
x
n
{\displaystyle f(x)=\sum _{n=0}^{\infty }a_{n}x^{n}}
that is convergent for real x in the open interval (0, 1), the value
lim
x
→
1
−
∑
n
=
0
∞
a
n
x
n
{\displaystyle \lim _{x\rightarrow 1^{-}}\sum _{n=0}^{\infty }a_{n}x^{n}}
, which is assigned to
f
(
1
)
=
∑
n
=
0
∞
a
n
{\displaystyle f(1)=\sum _{n=0}^{\infty }a_{n}}
by the Abel summation method (or A-method).