multinomial theorem

A multinomial is a mathematical expression consisting of two or more terms, e.g.


The multinomial theorem provides the general form of the expansion of the powers of this expression, in the process specifying the multinomial coefficientsDlmfMathworld which are found in that expansion. The expansion is:

(x1+x2++xk)n=n!n1!n2!nk!x1n1x2n2xknk (1)

where the sum is taken over all multi-indices (n1,nk)k that sum to n.

The expression n!n1!n2!nk! occurring in the expansion is called multinomial coefficient and is denoted by

Title multinomial theorem
Canonical name MultinomialTheorem
Date of creation 2013-03-22 13:13:05
Last modified on 2013-03-22 13:13:05
Owner bshanks (153)
Last modified by bshanks (153)
Numerical id 12
Author bshanks (153)
Entry type Theorem
Classification msc 05A10
Related topic BinomialFormula
Related topic BinomialCoefficient
Related topic GeneralizedLeibnizRule
Related topic NthDerivativeOfADeterminant
Defines multinomial
Defines multinomial coefficient