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}] > Representations through more general functions > Through other functions > Involving some hypergeometric-type functions





http://functions.wolfram.com/07.38.26.0004.01









  


  








Input Form





ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {j, m}] == KroneckerDelta[m, Subscript[m, 1] + Subscript[m, 2]] (-1)^(4 Subscript[j, 2]) Sqrt[1 + 2 j] Sqrt[Gamma[1 - 2 Subscript[j, 1] + 2 Subscript[j, 2]]] Sqrt[Gamma[2 - Subscript[j, 1] + 4 Subscript[j, 2] + Subscript[m, 1]]] Sqrt[Gamma[2 + 3 Subscript[j, 2] - Subscript[m, 2]]] (SixJSymbol[{2 Subscript[j, 2] - Subscript[j, 1], Subscript[j, 2], j}, {-((m + j + 1)/2), (m - j - 1)/2, (Subscript[m, 1] - Subscript[m, 2] - Subscript[j, 1] + 3 Subscript[j, 2])/2}]/ (Sqrt[Gamma[2 + 4 Subscript[j, 2]]] Sqrt[Gamma[1 - Subscript[j, 1] + 2 Subscript[j, 2] + Subscript[m, 1]]] Sqrt[Gamma[1 - 2 Subscript[j, 1] + 3 Subscript[j, 2] - Subscript[m, 2]]])) /; j + Subscript[j, 1] + Subscript[j, 2] == -1








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ClebschGordan", "[", 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["j", ",", "m"]], "}"]]]], "]"]], "\[Equal]", " ", RowBox[List[RowBox[List["KroneckerDelta", "[", RowBox[List["m", ",", RowBox[List[SubscriptBox["m", "1"], "+", SubscriptBox["m", "2"]]]]], "]"]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", " ", SubscriptBox["j", "2"]]]], SqrtBox[RowBox[List["1", "+", RowBox[List["2", " ", "j"]]]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", RowBox[List["2", " ", SubscriptBox["j", "1"]]], "+", RowBox[List["2", " ", SubscriptBox["j", "2"]]]]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["2", "-", SubscriptBox["j", "1"], "+", RowBox[List["4", " ", SubscriptBox["j", "2"]]], "+", SubscriptBox["m", "1"]]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["2", "+", RowBox[List["3", " ", SubscriptBox["j", "2"]]], "-", SubscriptBox["m", "2"]]], "]"]]], " ", RowBox[List[RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["2", " ", SubscriptBox["j", "2"]]], "-", SubscriptBox["j", "1"]]], ",", SubscriptBox["j", "2"], ",", "j"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["m", "+", "j", "+", "1"]], "2"]]], " ", ",", FractionBox[RowBox[List["m", "-", "j", "-", "1"]], "2"], " ", ",", FractionBox[RowBox[List[SubscriptBox["m", "1"], "-", SubscriptBox["m", "2"], "-", SubscriptBox["j", "1"], "+", RowBox[List["3", " ", SubscriptBox["j", "2"]]]]], "2"]]], " ", "}"]]]], "]"]], "/", RowBox[List["(", " ", RowBox[List[SqrtBox[RowBox[List[" ", RowBox[List["Gamma", "[", RowBox[List["2", "+", RowBox[List["4", " ", SubscriptBox["j", "2"]]]]], "]"]]]]], SqrtBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["j", "1"], "+", RowBox[List["2", " ", SubscriptBox["j", "2"]]], "+", SubscriptBox["m", "1"]]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", RowBox[List["2", " ", SubscriptBox["j", "1"]]], "+", RowBox[List["3", " ", SubscriptBox["j", "2"]]], "-", SubscriptBox["m", "2"]]], "]"]]]]], ")"]]]]]]]], "/;", RowBox[List[RowBox[List["j", "+", SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"]]], "\[Equal]", RowBox[List["-", "1"]]]]]]]]








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> &#9001; </mo> <mrow> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> j </mi> <mn> 2 </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> 2 </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> 2 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <mi> j </mi> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <mi> m </mi> </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;2&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;m&quot;, &quot;1&quot;], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;m&quot;, &quot;2&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;2&quot;], &quot;\[MediumSpace]&quot;, &quot;j&quot;, &quot;\[MediumSpace]&quot;, &quot;m&quot;]]]], &quot;\[RightAngleBracket]&quot;]], ClebschGordan, Rule[StripWrapperBoxes, True]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <msub> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <mi> m </mi> <mo> , </mo> <mrow> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> </mrow> </msub> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> j </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> - </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </msqrt> </mrow> <mrow> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> - </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </msqrt> </mrow> </mfrac> <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> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> </mtd> <mtd> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <mi> j </mi> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> j </mi> <mo> + </mo> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> j </mi> </mrow> <mo> + </mo> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </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> <mo> /; </mo> <mrow> <mrow> <mi> j </mi> <mo> + </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <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'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </list> <list> <ci> j </ci> <ci> m </ci> </list> </apply> <apply> <times /> <apply> <ci> KroneckerDelta </ci> <ci> m </ci> <apply> <plus /> <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> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> j </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> SixJSymbol </ci> <list> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <ci> j </ci> </list> <list> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> j </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </list> </apply> </apply> </apply> <apply> <eq /> <apply> <plus /> <ci> j </ci> <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> <cn type='integer'> -1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ClebschGordan", "[", 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["j", ",", "m_"]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["KroneckerDelta", "[", RowBox[List["m", ",", RowBox[List[SubscriptBox["mm", "1"], "+", SubscriptBox["mm", "2"]]]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", " ", SubscriptBox["j", "2"]]]], " ", SqrtBox[RowBox[List["1", "+", RowBox[List["2", " ", "j"]]]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", RowBox[List["2", " ", SubscriptBox["j", "1"]]], "+", RowBox[List["2", " ", SubscriptBox["j", "2"]]]]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["2", "-", SubscriptBox["j", "1"], "+", RowBox[List["4", " ", SubscriptBox["j", "2"]]], "+", SubscriptBox["mm", "1"]]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["2", "+", RowBox[List["3", " ", SubscriptBox["j", "2"]]], "-", SubscriptBox["mm", "2"]]], "]"]]], " ", RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["2", " ", SubscriptBox["j", "2"]]], "-", SubscriptBox["j", "1"]]], ",", SubscriptBox["j", "2"], ",", "j"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["m", "+", "j", "+", "1"]], ")"]]]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["m", "-", "j", "-", "1"]], ")"]]]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[SubscriptBox["mm", "1"], "-", SubscriptBox["mm", "2"], "-", SubscriptBox["j", "1"], "+", RowBox[List["3", " ", SubscriptBox["j", "2"]]]]], ")"]]]]]], "}"]]]], "]"]]]], RowBox[List[SqrtBox[RowBox[List["Gamma", "[", RowBox[List["2", "+", RowBox[List["4", " ", SubscriptBox["j", "2"]]]]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["j", "1"], "+", RowBox[List["2", " ", SubscriptBox["j", "2"]]], "+", SubscriptBox["mm", "1"]]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", RowBox[List["2", " ", SubscriptBox["j", "1"]]], "+", RowBox[List["3", " ", SubscriptBox["j", "2"]]], "-", SubscriptBox["mm", "2"]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["j", "+", SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"]]], "\[Equal]", RowBox[List["-", "1"]]]]]]]]]]


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





2001-10-29