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
 











Binomial




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Binomial[n,k] > Identities > Functional identities > Relations of special kind





http://functions.wolfram.com/06.03.17.0003.01









  


  








Input Form





Binomial[Subscript[z, 1] - Subscript[z, 2], Subscript[z, 4] - Subscript[z, 2]] Binomial[Subscript[z, 1] - Subscript[z, 3], Subscript[z, 4]] Binomial[Subscript[z, 1] - Subscript[z, 2] - Subscript[z, 3], Subscript[z, 4] - Subscript[z, 3]] == Binomial[Subscript[z, 1] - Subscript[z, 2], Subscript[z, 4]] Binomial[Subscript[z, 1] - Subscript[z, 3], Subscript[z, 4] - Subscript[z, 3]] Binomial[Subscript[z, 1] - Subscript[z, 2] - Subscript[z, 3], Subscript[z, 4] - Subscript[z, 2]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List[SubscriptBox["z", "1"], "-", SubscriptBox["z", "2"]]], ",", RowBox[List[SubscriptBox["z", "4"], "-", SubscriptBox["z", "2"]]]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List[SubscriptBox["z", "1"], "-", SubscriptBox["z", "3"]]], ",", SubscriptBox["z", "4"]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List[SubscriptBox["z", "1"], "-", SubscriptBox["z", "2"], "-", SubscriptBox["z", "3"]]], ",", RowBox[List[SubscriptBox["z", "4"], "-", SubscriptBox["z", "3"]]]]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List[SubscriptBox["z", "1"], "-", SubscriptBox["z", "2"]]], ",", SubscriptBox["z", "4"]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List[SubscriptBox["z", "1"], "-", SubscriptBox["z", "3"]]], ",", RowBox[List[SubscriptBox["z", "4"], "-", SubscriptBox["z", "3"]]]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List[SubscriptBox["z", "1"], "-", SubscriptBox["z", "2"], "-", SubscriptBox["z", "3"]]], ",", RowBox[List[SubscriptBox["z", "4"], "-", SubscriptBox["z", "2"]]]]], "]"]]]]]]]]








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> <mtable> <mtr> <mtd> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> z </mi> <mn> 4 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;1&quot;], &quot;-&quot;, SubscriptBox[&quot;z&quot;, &quot;2&quot;]]], Identity, Rule[Editable, True]]], List[TagBox[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;4&quot;], &quot;-&quot;, SubscriptBox[&quot;z&quot;, &quot;2&quot;]]], Identity, Rule[Editable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 3 </mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi> z </mi> <mn> 4 </mn> </msub> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;1&quot;], &quot;-&quot;, SubscriptBox[&quot;z&quot;, &quot;3&quot;]]], Identity, Rule[Editable, True]]], List[TagBox[SubscriptBox[&quot;z&quot;, &quot;4&quot;], Identity, Rule[Editable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 3 </mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> z </mi> <mn> 4 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 3 </mn> </msub> </mrow> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;1&quot;], &quot;-&quot;, SubscriptBox[&quot;z&quot;, &quot;2&quot;], &quot;-&quot;, SubscriptBox[&quot;z&quot;, &quot;3&quot;]]], Identity, Rule[Editable, True]]], List[TagBox[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;4&quot;], &quot;-&quot;, SubscriptBox[&quot;z&quot;, &quot;3&quot;]]], Identity, Rule[Editable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> </mrow> <mo> &#10869; </mo> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi> z </mi> <mn> 4 </mn> </msub> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;1&quot;], &quot;-&quot;, SubscriptBox[&quot;z&quot;, &quot;2&quot;]]], Identity, Rule[Editable, True]]], List[TagBox[SubscriptBox[&quot;z&quot;, &quot;4&quot;], Identity, Rule[Editable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 3 </mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> z </mi> <mn> 4 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 3 </mn> </msub> </mrow> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;1&quot;], &quot;-&quot;, SubscriptBox[&quot;z&quot;, &quot;3&quot;]]], Identity, Rule[Editable, True]]], List[TagBox[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;4&quot;], &quot;-&quot;, SubscriptBox[&quot;z&quot;, &quot;3&quot;]]], Identity, Rule[Editable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 3 </mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> z </mi> <mn> 4 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;1&quot;], &quot;-&quot;, SubscriptBox[&quot;z&quot;, &quot;2&quot;], &quot;-&quot;, SubscriptBox[&quot;z&quot;, &quot;3&quot;]]], Identity, Rule[Editable, True]]], List[TagBox[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;4&quot;], &quot;-&quot;, SubscriptBox[&quot;z&quot;, &quot;2&quot;]]], Identity, Rule[Editable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <ci> Binomial </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <ci> Binomial </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Binomial </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <ci> Binomial </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List[SubscriptBox["z_", "1"], "-", SubscriptBox["z_", "2"]]], ",", RowBox[List[SubscriptBox["z_", "4"], "-", SubscriptBox["z_", "2"]]]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List[SubscriptBox["z_", "1"], "-", SubscriptBox["z_", "3"]]], ",", SubscriptBox["z_", "4"]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List[SubscriptBox["z_", "1"], "-", SubscriptBox["z_", "2"], "-", SubscriptBox["z_", "3"]]], ",", RowBox[List[SubscriptBox["z_", "4"], "-", SubscriptBox["z_", "3"]]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List[SubscriptBox["zz", "1"], "-", SubscriptBox["zz", "2"]]], ",", SubscriptBox["zz", "4"]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List[SubscriptBox["zz", "1"], "-", SubscriptBox["zz", "3"]]], ",", RowBox[List[SubscriptBox["zz", "4"], "-", SubscriptBox["zz", "3"]]]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List[SubscriptBox["zz", "1"], "-", SubscriptBox["zz", "2"], "-", SubscriptBox["zz", "3"]]], ",", RowBox[List[SubscriptBox["zz", "4"], "-", SubscriptBox["zz", "2"]]]]], "]"]]]]]]]]


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





2001-10-29