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In mathematics, the multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization...

Multinomial may refer to: Multinomial theorem, and the multinomial coefficient Multinomial distribution Multinomial logistic regression Multinomial test...

algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, the power ⁠ ( x...

In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts...

Pascal's triangle into arbitrary number of dimensions, based on the multinomial theorem. Let m (m > 0) be a number of terms of a polynomial and n (n ≥ 0)...

later rediscovered by Euler, is a very simple application of the multinomial theorem, which states ( x 1 + x 2 + ⋯ + x m ) n = ∑ k 1 , k 2 , … , k m k...

(Ramsey theory) Multinomial theorem (algebra, combinatorics) Mycielski's theorem (graph theory) Nicomachus's theorem (number theory) Ore's theorem (graph theory)...

representation of an integer Mahler's theorem Multinomial distribution Multinomial coefficient, Multinomial formula, Multinomial theorem Multiplicities of entries...

In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest...

In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more...

the quadratic kernel. After using the multinomial theorem (twice—the outermost application is the binomial theorem) and regrouping, K ( x , y ) = ( ∑ i...

dimensions; for σ = 1 {\displaystyle \sigma =1} , its expansion using the multinomial theorem is: exp ⁡ ( − 1 2 ‖ x − x ′ ‖ 2 ) = exp ⁡ ( 2 2 x ⊤ x ′ − 1 2 ‖ x...

In calculus, Taylor's theorem gives an approximation of a k {\textstyle k} -times differentiable function around a given point by a polynomial of degree...

1). That line will be the proportion.[further explanation needed] Multinomial theorem Trinomial expansion Pascal's triangle Pascal's simplex Staib, J.;...

approximation theorem Hilbert's paradox of the Grand Hotel Multinomial theorem Pochhammer symbol Ramsey's theorem Herstein 1964, p. 90 Rittaud, Benoît; Heeffer, Albrecht...

(or R n → R {\displaystyle \mathbb {R} ^{n}\to \mathbb {R} } ). Multinomial theorem ( ∑ i = 1 n x i ) k = ∑ | α | = k ( k α ) x α {\displaystyle \left(\sum...

combinatorisch-analytischer Abhandlungen, which contained a claim that de Moivre's multinomial theorem was “the most important proposition in all of mathematical analysis”...

de Moivre also generalised Newton's noteworthy binomial theorem into the multinomial theorem. The Royal Society became apprised of this method in 1697...

coefficients should not be confused with the multinomial coefficients that occur in the multinomial theorem. The value of multiset coefficients can be given...

In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite...