Binomial Series Definition

The Maclaurin series expansion of the function f(x) = (1 + x)^α, for arbitrary complex α; the series \textstyle\sum_{k=0}^\infty{\alpha \choose k} x^k, where \textstyle{\alpha \choose k} = \frac{\alpha(\alpha-1)(\alpha-2)\dots(\alpha-k+1)}{k!}.

The binomial theorem .