binomial series noun2 •The Maclaurin series expansion of the function f(x) = (1 + x)^α, for arbitrary complex α; the series ∑ₖ₌₀ ᪲α choose kxᵏ, where α choose k=(α(α-1)(α-2)…(α-k+1))/(k!).Thus, by the Ratio Test, the binomial series converges if |x| < 1 and diverges if |x| > 1. — 2010 •The binomial theorem.The binomial series or binomial theorem is a formula for raising a binomial expression to any power without lengthy multiplication. — 2017
