1.NounAn equation involving an ordered sequence of real numbers (
{
a
n
}
n
=
1
∞
{\displaystyle \left\{a_{n}\right\}_{n=1}^{\infty }}
) and some of its differences, where the first difference is defined as
Δ
(
a
n
)
=
a
n
+
1
−
a
n
{\displaystyle \Delta (a_{n})=a_{n+1}-a_{n}\,}
and the k difference is defined recursively as
Δ
k
(
a
n
)
=
Δ
k
−
1
(
a
n
+
1
)
−
Δ
k
−
1
(
a
n
)
{\displaystyle \Delta ^{k}(a_{n})=\Delta ^{k-1}(a_{n+1})-\Delta ^{k-1}(a_{n})\,}
.