This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Multinomial

 Multinomialgives the multinomial coefficient .
• Integer mathematical function, suitable for both symbolic and numerical manipulation.
• The multinomial coefficient Multinomial, denoted , gives the number of ways of partitioning distinct objects into sets, each of size (with ).
The 1, 2, 1 multinomial coefficient appears as the coefficient of :
 Out[1]=
The 1, 2, 1 multinomial coefficient appears as the coefficient of :
 Out[2]=
 Scope   (8)
Special cases evaluate for symbolic arguments:
Evaluate with any number of arguments:
Evaluate for large integer arguments:
Evaluate for half-integer arguments:
Numerical generalization:
Evaluate for complex arguments:
Series expansion at a generic point:
 Applications   (4)
Illustrate the multinomial theorem:
Plot isosurfaces of the number of ways to put elements in three boxes:
Multinomial probability distribution:
Volume of a hyper-super-ellipsoid is :
Compare with direct integration:
With two arguments, Multinomial gives binomial coefficients:
Use FullSimplify to simplify expressions involving multinomial coefficients:
Use FunctionExpand to expand into Gamma functions:
Large arguments can give results too large to be computed explicitly:
Machine-number inputs can give high-precision results:
As a multivariate function, Multinomial is not continuous in all variables at negative integers:
Trinomials mod 2:
Modulo 3:
Nested multinomials over the complex plane:
Plot Multinomial for complex arguments:
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