Binomial series

Noun

Definitions

1.NounThe 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!}}} .

2.NounThe binomial theorem.

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