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binomial product

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  • 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 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 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

  • Product rule — For Euler s chain rule relating partial derivatives of three independent variables, see Triple product rule. For the counting principle in combinatorics, see Rule of product. Topics in Calculus Fundamental theorem Limits of functions Continuity… …   Wikipedia

  • Binomial — In elementary algebra, a binomial is a polynomial with two terms: the sum of two monomials. It is the simplest kind of polynomial except for a monomial.The binomial a^2 b^2 can be factored as the product of two other binomials:: a^2 b^2 = (a +… …   Wikipedia

  • Binomial distribution — Probability distribution name =Binomial type =mass pdf cdf Colors match the image above parameters =n geq 0 number of trials (integer) 0leq p leq 1 success probability (real) support =k in {0,dots,n}! pdf ={nchoose k} p^k (1 p)^{n k} ! cdf =I {1… …   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

  • Empty product — In mathematics, an empty product, or nullary product, is the result of multiplying no factors. It is equal to the multiplicative identity 1, given that it exists for the multiplication operation in question, just as the empty sum the result of… …   Wikipedia

  • Cauchy product — In mathematics, the Cauchy product, named after Augustin Louis Cauchy, of two sequences , , is the discrete convolution of the two sequences, the sequence whose general term is given by In other words, it is the sequence whose associated formal… …   Wikipedia

  • Wick product — In probability theory, the Wick product:langle X 1,dots,X k angle,named after physicist Gian Carlo Wick, is a sort of product of the random variables, X 1, ..., X k , defined recursively as follows::langle angle = 1,(i.e. the empty product… …   Wikipedia

  • Leibniz rule (generalized product rule) — In calculus, the Leibniz rule, named after Gottfried Leibniz, generalizes the product rule. It states that if f and g are n times differentiable functions, then the n th derivative of the product fg is given by:(f cdot g)^{(n)}=sum {k=0}^n {n… …   Wikipedia

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