Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











Multinomial




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Multinomial[n1,n2,...,nm] > General characteristics > Symmetries and periodicities > Permutation symmetry





http://functions.wolfram.com/06.04.04.0004.01









  


  








Input Form





Multinomial[Subscript[n, 1], Subscript[n, 2], \[Ellipsis], Subscript[n, k], \[Ellipsis], Subscript[n, j], \[Ellipsis], Subscript[n, m]] == Multinomial[Subscript[n, 1], Subscript[n, 2], \[Ellipsis], Subscript[n, j], \[Ellipsis], Subscript[n, k], \[Ellipsis], Subscript[n, m]] /; Subscript[n, k] != Subscript[n, j] && k != j








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Multinomial", "[", RowBox[List[SubscriptBox["n", "1"], ",", SubscriptBox["n", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["n", "k"], ",", "\[Ellipsis]", ",", SubscriptBox["n", "j"], ",", "\[Ellipsis]", ",", SubscriptBox["n", "m"]]], "]"]], "\[Equal]", RowBox[List["Multinomial", "[", RowBox[List[SubscriptBox["n", "1"], ",", SubscriptBox["n", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["n", "j"], ",", "\[Ellipsis]", ",", SubscriptBox["n", "k"], ",", "\[Ellipsis]", ",", SubscriptBox["n", "m"]]], "]"]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["n", "k"], "\[NotEqual]", SubscriptBox["n", "j"]]], "\[And]", RowBox[List["k", "\[NotEqual]", "j"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> n </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> n </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mo> &#8230; </mo> <mo> + </mo> <msub> <mi> n </mi> <mi> k </mi> </msub> <mo> + </mo> <mo> &#8230; </mo> <mo> + </mo> <msub> <mi> n </mi> <mi> j </mi> </msub> <mo> + </mo> <mo> &#8230; </mo> <mo> + </mo> <msub> <mi> n </mi> <mi> m </mi> </msub> </mrow> <mo> ; </mo> <msub> <mi> n </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> n </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> n </mi> <mi> k </mi> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> n </mi> <mi> j </mi> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> n </mi> <mi> m </mi> </msub> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[RowBox[List[SubscriptBox[&quot;n&quot;, &quot;1&quot;], &quot;+&quot;, SubscriptBox[&quot;n&quot;, &quot;2&quot;], &quot;+&quot;, &quot;\[Ellipsis]&quot;, &quot;+&quot;, SubscriptBox[&quot;n&quot;, &quot;k&quot;], &quot;+&quot;, &quot;\[Ellipsis]&quot;, &quot;+&quot;, SubscriptBox[&quot;n&quot;, &quot;j&quot;], &quot;+&quot;, &quot;\[Ellipsis]&quot;, &quot;+&quot;, SubscriptBox[&quot;n&quot;, &quot;m&quot;]]], &quot;;&quot;, SubscriptBox[&quot;n&quot;, &quot;1&quot;]]], &quot;,&quot;, SubscriptBox[&quot;n&quot;, &quot;2&quot;], &quot;,&quot;, &quot;\[Ellipsis]&quot;, &quot;,&quot;, SubscriptBox[&quot;n&quot;, &quot;k&quot;], &quot;,&quot;, &quot;\[Ellipsis]&quot;, &quot;,&quot;, SubscriptBox[&quot;n&quot;, &quot;j&quot;], &quot;,&quot;, &quot;\[Ellipsis]&quot;, &quot;,&quot;, SubscriptBox[&quot;n&quot;, &quot;m&quot;]]], &quot;)&quot;]], Multinomial, Rule[Editable, True]] </annotation> </semantics> <mo> &#10869; </mo> <semantics> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> n </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> n </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mo> &#8230; </mo> <mo> + </mo> <msub> <mi> n </mi> <mi> j </mi> </msub> <mo> + </mo> <mo> &#8230; </mo> <mo> + </mo> <msub> <mi> n </mi> <mi> k </mi> </msub> <mo> + </mo> <mo> &#8230; </mo> <mo> + </mo> <msub> <mi> n </mi> <mi> m </mi> </msub> </mrow> <mo> ; </mo> <msub> <mi> n </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> n </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> n </mi> <mi> j </mi> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> n </mi> <mi> k </mi> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> n </mi> <mi> m </mi> </msub> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[RowBox[List[SubscriptBox[&quot;n&quot;, &quot;1&quot;], &quot;+&quot;, SubscriptBox[&quot;n&quot;, &quot;2&quot;], &quot;+&quot;, &quot;\[Ellipsis]&quot;, &quot;+&quot;, SubscriptBox[&quot;n&quot;, &quot;j&quot;], &quot;+&quot;, &quot;\[Ellipsis]&quot;, &quot;+&quot;, SubscriptBox[&quot;n&quot;, &quot;k&quot;], &quot;+&quot;, &quot;\[Ellipsis]&quot;, &quot;+&quot;, SubscriptBox[&quot;n&quot;, &quot;m&quot;]]], &quot;;&quot;, SubscriptBox[&quot;n&quot;, &quot;1&quot;]]], &quot;,&quot;, SubscriptBox[&quot;n&quot;, &quot;2&quot;], &quot;,&quot;, &quot;\[Ellipsis]&quot;, &quot;,&quot;, SubscriptBox[&quot;n&quot;, &quot;j&quot;], &quot;,&quot;, &quot;\[Ellipsis]&quot;, &quot;,&quot;, SubscriptBox[&quot;n&quot;, &quot;k&quot;], &quot;,&quot;, &quot;\[Ellipsis]&quot;, &quot;,&quot;, SubscriptBox[&quot;n&quot;, &quot;m&quot;]]], &quot;)&quot;]], Multinomial, Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> n </mi> <mi> k </mi> </msub> <mo> &#8800; </mo> <msub> <mi> n </mi> <mi> j </mi> </msub> </mrow> <mo> &#8743; </mo> <mrow> <mi> k </mi> <mo> &#8800; </mo> <mi> j </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> Multinomial </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> k </ci> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> j </ci> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> m </ci> </apply> </apply> <apply> <ci> Multinomial </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> j </ci> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> k </ci> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <and /> <apply> <neq /> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> k </ci> </apply> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> j </ci> </apply> </apply> <apply> <neq /> <ci> k </ci> <ci> j </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Multinomial", "[", RowBox[List[SubscriptBox["n_", "1"], ",", SubscriptBox["n_", "2"], ",", "\[Ellipsis]_", ",", SubscriptBox["n_", "k_"], ",", "\[Ellipsis]_", ",", SubscriptBox["n_", "j_"], ",", "\[Ellipsis]_", ",", SubscriptBox["n_", "m_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Multinomial", "[", RowBox[List[SubscriptBox["nn", "1"], ",", SubscriptBox["nn", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["nn", "j"], ",", "\[Ellipsis]", ",", SubscriptBox["nn", "k"], ",", "\[Ellipsis]", ",", SubscriptBox["nn", "m"]]], "]"]], "/;", RowBox[List[RowBox[List[SubscriptBox["nn", "k"], "\[NotEqual]", SubscriptBox["nn", "j"]]], "&&", RowBox[List["k", "\[NotEqual]", "j"]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29