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ThreeJSymbol




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ThreeJSymbol[{j1,m1},{j2,m2},{j3,m3}] > Integral representations > Multiple integral representations > Involving the direct function





http://functions.wolfram.com/07.39.07.0008.01









  


  








Input Form





ThreeJSymbol[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 3], Subscript[m, 3]}] ThreeJSymbol[{Subscript[j, 1], Subscript[n, 1]}, {Subscript[j, 2], Subscript[n, 2]}, {Subscript[j, 3], Subscript[n, 3]}] == ((-1)^(-Subscript[m, 3] + Subscript[n, 3])/ (8 Pi^2)) Integrate[Sin[\[Beta]] WignerD[Subscript[m, 1], Subscript[n, 1], Subscript[j, 1], \[Alpha], \[Beta], \[Gamma]] WignerD[Subscript[m, 2], Subscript[n, 2], Subscript[j, 2], \[Alpha], \[Beta], \[Gamma]] Conjugate[WignerD[-Subscript[m, 3], -Subscript[n, 3], Subscript[j, 3], \[Alpha], \[Beta], \[Gamma]]], {\[Alpha], 0, 2 Pi}, {\[Beta], 0, Pi}, {\[Gamma], 0, 2 Pi}] /; \[ScriptCapitalP]\[ScriptH]\[ScriptY]\[ScriptS]\[ScriptI]\[ScriptC]\ \[ScriptA]\[ScriptL]\[ScriptCapitalQ][{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 3], Subscript[m, 3]}] && \[ScriptCapitalP]\[ScriptH]\[ScriptY]\[ScriptS]\[ScriptI]\[ScriptC]\ \[ScriptA]\[ScriptL]\[ScriptCapitalQ][{Subscript[j, 1], Subscript[n, 1]}, {Subscript[j, 2], Subscript[n, 2]}, {Subscript[j, 3], Subscript[n, 3]}]








Standard Form





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MathML Form







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</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> 2 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi> n </mi> <mn> 1 </mn> </msub> </mtd> <mtd> <msub> <mi> n </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <msub> <mi> n </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> </mrow> <mo> &#10869; 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Rule Form





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





2001-12-21