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

 

Developed with Mathematica -- Download a Free Trial Version
 











ClebschGordan




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Summation > Finite summation > Involving three Clebsch Gordan coefficients





http://functions.wolfram.com/07.38.23.0017.01









  


  








Input Form





Sum[ClebschGordan[{Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 3], Subscript[m, 3]}] ClebschGordan[{Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 6], Subscript[m, 6]}, {Subscript[j, 4], Subscript[m, 4]}] ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 5], Subscript[m, 5]}, {Subscript[j, 6], Subscript[m, 6]}], {Subscript[m, 1], -Subscript[j, 1], Subscript[j, 1]}, {Subscript[m, 2], -Subscript[j, 2], Subscript[j, 2]}, {Subscript[m, 6], -Subscript[j, 6], Subscript[j, 6]}] == (-1)^(Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 4] + Subscript[j, 5]) Sqrt[2 Subscript[j, 3] + 1] Sqrt[2 Subscript[j, 6] + 1] ClebschGordan[{Subscript[j, 3], Subscript[m, 3]}, {Subscript[j, 5], Subscript[m, 5]}, {Subscript[j, 4], Subscript[m, 4]}] SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 4], Subscript[j, 5], Subscript[j, 6]}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "1"], "=", RowBox[List["-", SubscriptBox["j", "1"]]]]], SubscriptBox["j", "1"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "2"], "=", RowBox[List["-", SubscriptBox["j", "2"]]]]], SubscriptBox["j", "2"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "6"], "=", RowBox[List["-", SubscriptBox["j", "6"]]]]], SubscriptBox["j", "6"]], RowBox[List[RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["m", "3"]]], "}"]]]], "]"]], RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox["m", "6"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox["m", "4"]]], "}"]]]], "]"]], RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox["m", "5"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox["m", "6"]]], "}"]]]], "]"]]]]]]]]]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "5"]]]], SqrtBox[RowBox[List[RowBox[List["2", SubscriptBox["j", "3"]]], "+", "1"]]], SqrtBox[RowBox[List[RowBox[List["2", SubscriptBox["j", "6"]]], "+", "1"]]], RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["m", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox["m", "5"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox["m", "4"]]], "}"]]]], "]"]], RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "2"], ",", SubscriptBox["j", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox["j", "5"], ",", SubscriptBox["j", "6"]]], "}"]]]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> </mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> </mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> m </mi> <mn> 6 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> </mrow> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </munderover> <mrow> <semantics> <mrow> <mo> &#9001; </mo> <mrow> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mrow> <mtext> &#8287; </mtext> <mo> &#10072; </mo> <mtext> &#8287; </mtext> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> m </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> &#9002; </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[LeftAngleBracket]&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;j&quot;, &quot;2&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;j&quot;, &quot;1&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;m&quot;, &quot;2&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;m&quot;, &quot;1&quot;]]], &quot;\[MediumSpace]&quot;, &quot;\[VerticalSeparator]&quot;, &quot;\[MediumSpace]&quot;, RowBox[List[SubscriptBox[&quot;j&quot;, &quot;2&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;j&quot;, &quot;1&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;j&quot;, &quot;3&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;m&quot;, &quot;3&quot;]]]]], &quot;\[RightAngleBracket]&quot;]], ClebschGordan, Rule[StripWrapperBoxes, True]] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <mrow> <mo> &#9001; </mo> <mrow> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> j </mi> <mn> 6 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> m </mi> <mn> 6 </mn> </msub> </mrow> <mtext> &#8287; </mtext> <mo> &#10072; </mo> <mtext> &#8287; </mtext> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> j </mi> <mn> 6 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> m </mi> <mn> 4 </mn> </msub> </mrow> </mrow> <mo> &#9002; </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[LeftAngleBracket]&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;j&quot;, &quot;2&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;j&quot;, &quot;6&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;m&quot;, &quot;2&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;m&quot;, &quot;6&quot;]]], &quot;\[MediumSpace]&quot;, &quot;\[VerticalSeparator]&quot;, &quot;\[MediumSpace]&quot;, RowBox[List[SubscriptBox[&quot;j&quot;, &quot;2&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;j&quot;, &quot;6&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;j&quot;, &quot;4&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;m&quot;, &quot;4&quot;]]]]], &quot;\[RightAngleBracket]&quot;]], ClebschGordan, Rule[StripWrapperBoxes, True]] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <mrow> <mo> &#9001; </mo> <mrow> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> m </mi> <mn> 5 </mn> </msub> </mrow> <mtext> &#8287; </mtext> <mo> &#10072; </mo> <mtext> &#8287; </mtext> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> j </mi> <mn> 6 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> m </mi> <mn> 6 </mn> </msub> </mrow> </mrow> <mo> &#9002; </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[LeftAngleBracket]&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;j&quot;, &quot;1&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;j&quot;, &quot;5&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;m&quot;, &quot;1&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;m&quot;, &quot;5&quot;]]], &quot;\[MediumSpace]&quot;, &quot;\[VerticalSeparator]&quot;, &quot;\[MediumSpace]&quot;, RowBox[List[SubscriptBox[&quot;j&quot;, &quot;1&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;j&quot;, &quot;5&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;j&quot;, &quot;6&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;m&quot;, &quot;6&quot;]]]]], &quot;\[RightAngleBracket]&quot;]], ClebschGordan, Rule[StripWrapperBoxes, True]] </annotation> </semantics> </mrow> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <semantics> <mrow> <mo> &#9001; </mo> <mrow> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> m </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> m </mi> <mn> 5 </mn> </msub> </mrow> <mtext> &#8287; </mtext> <mo> &#10072; </mo> <mtext> &#8287; </mtext> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> m </mi> <mn> 4 </mn> </msub> </mrow> </mrow> <mo> &#9002; </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[LeftAngleBracket]&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;j&quot;, &quot;3&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;j&quot;, &quot;5&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;m&quot;, &quot;3&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;m&quot;, &quot;5&quot;]]], &quot;\[MediumSpace]&quot;, &quot;\[VerticalSeparator]&quot;, &quot;\[MediumSpace]&quot;, RowBox[List[SubscriptBox[&quot;j&quot;, &quot;3&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;j&quot;, &quot;5&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;j&quot;, &quot;4&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;m&quot;, &quot;4&quot;]]]]], &quot;\[RightAngleBracket]&quot;]], ClebschGordan, Rule[StripWrapperBoxes, True]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <semantics> <mo> { </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;{&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], SixJSymbol] </annotation> </semantics> <mtext> &#8287; </mtext> <mtable> <mtr> <mtd> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mtd> </mtr> </mtable> <mtext> &#8287; </mtext> <semantics> <mo> } </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;}&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], SixJSymbol] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 6 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </apply> </lowlimit> <uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> </lowlimit> <uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> </lowlimit> <uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </uplimit> <apply> <times /> <apply> <ci> ClebschGordan </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> <apply> <ci> ClebschGordan </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 6 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> </list> </apply> <apply> <ci> ClebschGordan </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 5 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 6 </cn> </apply> </list> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> ClebschGordan </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 5 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> </list> </apply> <apply> <ci> SixJSymbol </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </list> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m_", "1"], "=", RowBox[List["-", SubscriptBox["j", "1"]]]]], SubscriptBox["j", "1"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m_", "2"], "=", RowBox[List["-", SubscriptBox["j", "2"]]]]], SubscriptBox["j", "2"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m_", "6"], "=", RowBox[List["-", SubscriptBox["j", "6"]]]]], SubscriptBox["j", "6"]], RowBox[List[RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m_", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["m_", "3"]]], "}"]]]], "]"]], " ", RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox["m_", "6"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox["m_", "4"]]], "}"]]]], "]"]], " ", RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m_", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox["m_", "5"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox["m_", "6"]]], "}"]]]], "]"]]]]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "5"]]]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", SubscriptBox["j", "3"]]], "+", "1"]]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", SubscriptBox["j", "6"]]], "+", "1"]]], " ", RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["mm", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox["mm", "5"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox["mm", "4"]]], "}"]]]], "]"]], " ", RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "2"], ",", SubscriptBox["j", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox["j", "5"], ",", SubscriptBox["j", "6"]]], "}"]]]], "]"]]]]]]]]


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





2001-12-21