binomial series

Fetched 2026-10-26 (cache).

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Noun

1. {{lb|en|mathematics}} The [[Maclaurin series]] expansion of the [[function]] ''f''(''x'') = (1 + ''x'')^''α'', for arbitrary [[complex]] ''α''; the series <math>\textstyle\sum_{k=0}^\infty{\alpha \choose k} x^k</math>, where <math>\textstyle{\alpha \choose k} = \frac{\alpha(\alpha-1)(\alpha-2)\dots(\alpha-k+1)}{k!}</math>.
2. {{lb|en|mathematics|loosely}} The [[binomial theorem]].

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