# binomial series

binomial series
an infinite series obtained by expanding a binomial raised to a power that is not a positive integer.
[1965-70]

* * *

Universalium. 2010.

### См. также в других словарях:

• 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 series — binominė eilutė statusas T sritis fizika atitikmenys: angl. binomial series vok. Binomialreihe, f; binomische Reihe, f rus. биномиальный ряд, m pranc. série binomiale, f …   Fizikos terminų žodynas

• binomial series — Math. an infinite series obtained by expanding a binomial raised to a power that is not a positive integer. Cf. binomial theorem. [1965 70] …   Useful english 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 — 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

• Series (mathematics) — A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely.[1] In mathematics, given an infinite sequence of numbers { an } …   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

• binomial coefficient — Math. any one of the coefficients of the variables in an expanded binomial series. Cf. binomial theorem. [1885 90] * * * …   Universalium

• Binomial type — In mathematics, a polynomial sequence, i.e., a sequence of polynomials indexed by { 0, 1, 2, 3, ... } in which the index of each polynomial equals its degree, is said to be of binomial type if it satisfies the sequence of identities:p n(x+y)=sum… …   Wikipedia

• Binomial transform — In combinatorial mathematics the binomial transform is a sequence transformation (ie, a transform of a sequence) that computes its forward differences. It is closely related to the Euler transform, which is the result of applying the binomial… …   Wikipedia

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