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
 











SixJSymbol






Mathematica Notation

Traditional Notation









Hypergeometric Functions > SixJSymbol[{j1,j2,j3},{j4,j5,j6}] > Representations through equivalent functions > With related functions





http://functions.wolfram.com/07.40.27.0001.01









  


  










Input Form





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










Standard Form





Cell[BoxData[RowBox[List[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"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "1"], "=", RowBox[List["-", SubscriptBox["j", "1"]]]]], SubscriptBox["j", "1"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox[OverscriptBox["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[OverscriptBox["m", "^"], "2"], "=", RowBox[List["-", SubscriptBox["j", "2"]]]]], SubscriptBox["j", "2"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "3"], "=", RowBox[List["-", SubscriptBox["j", "3"]]]]], SubscriptBox["j", "3"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox[OverscriptBox["m", "^"], "3"], "=", RowBox[List["-", SubscriptBox["j", "3"]]]]], SubscriptBox["j", "3"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "4"], "=", RowBox[List["-", SubscriptBox["j", "4"]]]]], SubscriptBox["j", "4"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox[OverscriptBox["m", "^"], "4"], "=", RowBox[List["-", SubscriptBox["j", "4"]]]]], SubscriptBox["j", "4"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "5"], "=", RowBox[List["-", SubscriptBox["j", "5"]]]]], SubscriptBox["j", "5"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox[OverscriptBox["m", "^"], "5"], "=", RowBox[List["-", SubscriptBox["j", "5"]]]]], SubscriptBox["j", "5"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "6"], "=", RowBox[List["-", SubscriptBox["j", "6"]]]]], SubscriptBox["j", "6"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox[OverscriptBox["m", "^"], "6"], "=", RowBox[List["-", SubscriptBox["j", "6"]]]]], SubscriptBox["j", "6"]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "5"], "+", SubscriptBox["j", "6"], "+", SubscriptBox["m", "1"], "+", SubscriptBox["m", "2"], "+", SubscriptBox["m", "3"], "+", SubscriptBox["m", "4"], "+", SubscriptBox["m", "5"], "+", SubscriptBox["m", "6"]]]], RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["m", "3"]]], "}"]]]], "]"]], RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox[OverscriptBox["m", "^"], "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox["m", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox[OverscriptBox["m", "^"], "6"]]], "}"]]]], "]"]], RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox[OverscriptBox["m", "^"], "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox[OverscriptBox["m", "^"], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox["m", "6"]]], "}"]]]], "]"]], RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox[OverscriptBox["m", "^"], "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox[OverscriptBox["m", "^"], "5"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox[OverscriptBox["m", "^"], "3"]]], "}"]]]], "]"]], RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["m", "1"], ",", RowBox[List["-", SubscriptBox[OverscriptBox["m", "^"], "1"]]]]], "]"]], RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["m", "2"], ",", RowBox[List["-", SubscriptBox[OverscriptBox["m", "^"], "2"]]]]], "]"]], RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["m", "3"], ",", RowBox[List["-", SubscriptBox[OverscriptBox["m", "^"], "3"]]]]], "]"]], RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["m", "4"], ",", RowBox[List["-", SubscriptBox[OverscriptBox["m", "^"], "4"]]]]], "]"]], RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["m", "5"], ",", RowBox[List["-", SubscriptBox[OverscriptBox["m", "^"], "5"]]]]], "]"]], RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["m", "6"], ",", RowBox[List["-", SubscriptBox[OverscriptBox["m", "^"], "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> <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> <mo> &#10869; </mo> <mrow> <mstyle minsize='3'> <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> </mstyle> <mrow> <mstyle minsize='3'> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <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> </mstyle> <mrow> <mstyle minsize='3'> <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> </mstyle> <mrow> <mstyle minsize='3'> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <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> </mstyle> <mrow> <mstyle minsize='3'> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> m </mi> <mn> 3 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </munderover> </mstyle> <mrow> <mstyle minsize='3'> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 3 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </munderover> </mstyle> <mrow> <mstyle minsize='3'> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> m </mi> <mn> 4 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mrow> </mrow> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </munderover> </mstyle> <mrow> <mstyle minsize='3'> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 4 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mrow> </mrow> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </munderover> </mstyle> <mrow> <mstyle minsize='3'> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> m </mi> <mn> 5 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> </mrow> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </munderover> </mstyle> <mrow> <mstyle minsize='3'> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 5 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> </mrow> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </munderover> </mstyle> <mrow> <mstyle minsize='3'> <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> </mstyle> <mrow> <mstyle minsize='3'> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <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> </mstyle> <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> 3 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> <mo> + </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> m </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> m </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> m </mi> <mn> 5 </mn> </msub> <mo> + </mo> <msub> <mi> m </mi> <mn> 6 </mn> </msub> </mrow> </msup> <mo> &#8290; </mo> <mrow> <semantics> <mo> ( </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;(&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </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> m </mi> <mn> 1 </mn> </msub> </mtd> <mtd> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <msub> <mi> m </mi> <mn> 3 </mn> </msub> </mtd> </mtr> </mtable> <mtext> &#8287; </mtext> <semantics> <mo> ) </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;)&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mo> ( </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;(&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> <mtext> &#8287; </mtext> <mtable> <mtr> <mtd> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 1 </mn> </msub> </mtd> <mtd> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 6 </mn> </msub> </mtd> </mtr> </mtable> <mtext> &#8287; </mtext> <semantics> <mo> ) </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;)&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mo> ( </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;(&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> <mtext> &#8287; </mtext> <mtable> <mtr> <mtd> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 4 </mn> </msub> </mtd> <mtd> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 2 </mn> </msub> </mtd> <mtd> <msub> <mi> m </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]]], ThreeJSymbol] </annotation> </semantics> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mo> ( </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;(&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> <mtext> &#8287; </mtext> <mtable> <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> 3 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 4 </mn> </msub> </mtd> <mtd> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 5 </mn> </msub> </mtd> <mtd> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 3 </mn> </msub> </mtd> </mtr> </mtable> <mtext> &#8287; </mtext> <semantics> <mo> ) </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;)&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> </mrow> <mo> &#8290; </mo> <msub> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mrow> <mo> - </mo> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 1 </mn> </msub> </mrow> </mrow> </msub> <mo> &#8290; </mo> <msub> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mrow> <mo> - </mo> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 2 </mn> </msub> </mrow> </mrow> </msub> <mo> &#8290; </mo> <msub> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <msub> <mi> m </mi> <mn> 3 </mn> </msub> <mo> , </mo> <mrow> <mo> - </mo> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 3 </mn> </msub> </mrow> </mrow> </msub> <mo> &#8290; </mo> <msub> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <msub> <mi> m </mi> <mn> 4 </mn> </msub> <mo> , </mo> <mrow> <mo> - </mo> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 4 </mn> </msub> </mrow> </mrow> </msub> <mo> &#8290; </mo> <msub> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <msub> <mi> m </mi> <mn> 5 </mn> </msub> <mo> , </mo> <mrow> <mo> - </mo> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 5 </mn> </msub> </mrow> </mrow> </msub> <mo> &#8290; </mo> <msub> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <msub> <mi> m </mi> <mn> 6 </mn> </msub> <mo> , </mo> <mrow> <mo> - </mo> <msub> <mover> <mi> m </mi> <mo> ^ </mo> </mover> <mn> 6 </mn> </msub> </mrow> </mrow> </msub> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <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> <sum /> <bvar> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <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'> 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> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <cn type='integer'> 5 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> </apply> </lowlimit> <uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 5 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> </apply> </lowlimit> <uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <cn type='integer'> 4 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> </apply> </lowlimit> <uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> </apply> </lowlimit> <uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <cn type='integer'> 3 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </apply> </lowlimit> <uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </apply> </lowlimit> <uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <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'> 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> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <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> <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> <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'> 3 </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> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 5 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <ci> ThreeJSymbol </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'> 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'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> <apply> <ci> ThreeJSymbol </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <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'> 2 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <cn type='integer'> 6 </cn> </apply> </list> </apply> <apply> <ci> ThreeJSymbol </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <cn type='integer'> 4 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <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> </apply> <apply> <ci> ThreeJSymbol </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <cn type='integer'> 4 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <cn type='integer'> 5 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <cn type='integer'> 3 </cn> </apply> </list> </apply> <apply> <ci> KroneckerDelta </ci> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <ci> KroneckerDelta </ci> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> KroneckerDelta </ci> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <ci> KroneckerDelta </ci> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <ci> KroneckerDelta </ci> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 5 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <ci> KroneckerDelta </ci> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 6 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <apply> <ci> OverHat </ci> <ci> m </ci> </apply> <cn type='integer'> 6 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", 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"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "1"], "=", RowBox[List["-", SubscriptBox["j", "1"]]]]], SubscriptBox["j", "1"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox[OverscriptBox["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[OverscriptBox["m", "^"], "2"], "=", RowBox[List["-", SubscriptBox["j", "2"]]]]], SubscriptBox["j", "2"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "3"], "=", RowBox[List["-", SubscriptBox["j", "3"]]]]], SubscriptBox["j", "3"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox[OverscriptBox["m", "^"], "3"], "=", RowBox[List["-", SubscriptBox["j", "3"]]]]], SubscriptBox["j", "3"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "4"], "=", RowBox[List["-", SubscriptBox["j", "4"]]]]], SubscriptBox["j", "4"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox[OverscriptBox["m", "^"], "4"], "=", RowBox[List["-", SubscriptBox["j", "4"]]]]], SubscriptBox["j", "4"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "5"], "=", RowBox[List["-", SubscriptBox["j", "5"]]]]], SubscriptBox["j", "5"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox[OverscriptBox["m", "^"], "5"], "=", RowBox[List["-", SubscriptBox["j", "5"]]]]], SubscriptBox["j", "5"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "6"], "=", RowBox[List["-", SubscriptBox["j", "6"]]]]], SubscriptBox["j", "6"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox[OverscriptBox["m", "^"], "6"], "=", RowBox[List["-", SubscriptBox["j", "6"]]]]], SubscriptBox["j", "6"]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "5"], "+", SubscriptBox["j", "6"], "+", SubscriptBox["m", "1"], "+", SubscriptBox["m", "2"], "+", SubscriptBox["m", "3"], "+", SubscriptBox["m", "4"], "+", SubscriptBox["m", "5"], "+", SubscriptBox["m", "6"]]]], " ", RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["m", "3"]]], "}"]]]], "]"]], " ", RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox[OverscriptBox["m", "^"], "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox["m", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox[OverscriptBox["m", "^"], "6"]]], "}"]]]], "]"]], " ", RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox[OverscriptBox["m", "^"], "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox[OverscriptBox["m", "^"], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox["m", "6"]]], "}"]]]], "]"]], " ", RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox[OverscriptBox["m", "^"], "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox[OverscriptBox["m", "^"], "5"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox[OverscriptBox["m", "^"], "3"]]], "}"]]]], "]"]], " ", RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["m", "1"], ",", RowBox[List["-", SubscriptBox[OverscriptBox["m", "^"], "1"]]]]], "]"]], " ", RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["m", "2"], ",", RowBox[List["-", SubscriptBox[OverscriptBox["m", "^"], "2"]]]]], "]"]], " ", RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["m", "3"], ",", RowBox[List["-", SubscriptBox[OverscriptBox["m", "^"], "3"]]]]], "]"]], " ", RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["m", "4"], ",", RowBox[List["-", SubscriptBox[OverscriptBox["m", "^"], "4"]]]]], "]"]], " ", RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["m", "5"], ",", RowBox[List["-", SubscriptBox[OverscriptBox["m", "^"], "5"]]]]], "]"]], " ", RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["m", "6"], ",", RowBox[List["-", SubscriptBox[OverscriptBox["m", "^"], "6"]]]]], "]"]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]










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





2001-10-29