binomial expansion

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• binomial expansion — noun : the expansion of a binomial …   Useful english dictionary

• Binomial theorem — The binomial coefficients appear as the entries of Pascal s triangle. In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power… …   Wikipedia

• binomial distribution — Statistics. a distribution giving the probability of obtaining a specified number of successes in a finite set of independent trials in which the probability of a success remains the same from trial to trial. Also called Bernoulli distribution.… …   Universalium

• binomial law — noun : a theorem in mathematics: the probability of an event whose probability on each trial is p occurring r times in n trials is given by the term containing pr in the binomial expansion of (p+q)n in which q=1 p * * * Genetics. See …   Useful english dictionary

• Binomial probability — typically deals with the probability of several successive decisions, each of which has two possible outcomes. Definition The probability of an event can be expressed as a binomial probability if its outcomes can be broken down into two… …   Wikipedia

• binomial theorem — n. the general formula for the expansion of any binomial when raised to a power that is a positive whole number; the expansion of (a + b) n: discovered by Omar Khayyám and generalized by Sir Isaac Newton (Ex.: (a + b) 2 = a2 + 2ab + b2) …   English World dictionary

• binomial coefficient — n. Math. 1. the coefficient of any term in the expansion of (x + a) n 2. the number of combinations of a specified size that can be drawn from a given set …   English World dictionary

• Binomial coefficient — The binomial coefficients can be arranged to form Pascal s triangle. In mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem. They are indexed by two nonnegative integers; the… …   Wikipedia

• binomial theorem — Math. the theorem giving the expansion of a binomial raised to any power. [1865 70] * * * In algebra, a formula for expansion of the binomial (x + y) raised to any positive integer power. A simple case is the expansion of (x + y)2, which is x2 +… …   Universalium

• Binomial series — In mathematics, the binomial series is the Taylor series at x = 0 of the function f given by f(x) = (1 + x) α, where α ∈ C is an arbitrary complex number. Explicitly, and the binomial series is the power series… …   Wikipedia

• binomial coefficient — noun : the coefficient of any term resulting from the expansion of the binomial (x+y)n * * * Math. any one of the coefficients of the variables in an expanded binomial series. Cf. binomial theorem. [1885 90] …   Useful english dictionary