Noun
Appell sequence (plural Appell sequences)
(mathematics) Any polynomial sequence
{
p
n
(
x
)
}
n
=
0
,
1
,
2
,
…
{\displaystyle \{p_{n}(x)\}_{n=0,1,2,\ldots }}
satisfying the identity
d
d
x
p
n
(
x
)
=
n
p
n
−
1
(
x
)
,
{\displaystyle {\frac {d}{dx}}p_{n}(x)=np_{n-1}(x),}
and in which
p
0
(
x
)
{\displaystyle p_{0}(x)}
is a non-zero constant.