Noun
(mathematics, loosely) The binomial theorem.
(mathematics) The Maclaurin series expansion of the function f(x) = (1 + x), for arbitrary complex α; the series
∑
k
=
0
∞
(
α
k
)
x
k
{\displaystyle \textstyle \sum _{k=0}^{\infty }{\alpha \choose k}x^{k}}
, where
(
α
k
)
=
α
(
α
−
1
)
(
α
−
2
)
…
(
α
−
k
+
1
)
k
!
{\displaystyle \textstyle {\alpha \choose k}={\frac {\alpha (\alpha -1)(\alpha -2)\dots (\alpha -k+1)}{k!}}}
.