multinomial theorem

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multinomial theorem

n.
The theorem that establishes the rule for forming the terms of the nth power of a sum of numbers in terms of products of powers of those numbers.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
References in periodicals archive ?
By the definition of the function [??] the value [??](z) equals the sum of multinomial coefficients M(k) over all integer vectors k that lie inside the n-dimensional simplex S(z) = {x : x [greater than or equal to] 0, [[summation].sup.n.sub.i=1] [a.sub.i][x.sub.i] [less than or equal to] z}:
where H(q) = - [[summation].sup.n.sub.i=1] [q.sub.i] ln [q.sub.i] (this correlation is closely connected with the so-called entropy inequality for multinomial coefficients).
The quantity of such words is defined by the multinomial coefficient