binomial identity

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• Binomial identity — may refer to:* Binomial theorem * Binomial type …   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

• 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 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 inverse theorem — In mathematics, the binomial inverse theorem is useful for expressing matrix inverses in different ways.If A, U, B, V are matrices of sizes p × p , p × q , q × q , q × p , respectively, then:left(mathbf{A}+mathbf{UBV} ight)^{ 1}=mathbf{A}^{ 1}… …   Wikipedia

• 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 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

• Q-Vandermonde identity — In mathematics, in the field of combinatorics, the q Vandermonde identity is the q analogue of the Chu Vandermonde identity:egin{bmatrix}m + nkend{bmatrix} q=sum {j} egin{bmatrix}mk jend{bmatrix} qegin{bmatrix}njend{bmatrix} qq^{j(m k+j)}.The… …   Wikipedia

• Vandermonde's identity — For the expression for a special determinant, see Vandermonde matrix. In combinatorics, Vandermonde s identity, or Vandermonde s convolution, named after Alexandre Théophile Vandermonde (1772), states that for binomial coefficients. This identity …   Wikipedia

• A curious identity involving binomial coefficients — In combinatorics, a curious identity by Sun is the following combinatorial identity involving binomial coefficients first established by Zhi Wei Sun in 2002::(x+m+1)sum {i=0}^m( 1)^idbinom{x+y+i}{m i}dbinom{y+2i}{i} sum {i=0}^{m}dbinom{x+i}{m i}( …   Wikipedia

• Dixon's identity — In mathematics, Dixon s identity (or Dixon s theorem or Dixon s formula) is any of several different but closely related identities proved by A. C. Dixon, some involving finite sums of products of three binomial coefficients, and some evaluating… …   Wikipedia