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ThreeJSymbol






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.39.07.0007.01









  


  










Input Form





ThreeJSymbol[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 3], Subscript[m, 3]}] == ((-1)^(Subscript[j, 2] - Subscript[j, 1] + Subscript[m, 3])/(8 Pi^2)) ((Sqrt[(Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 3] + 1)!] Sqrt[(Subscript[j, 1] + Subscript[j, 2] - Subscript[j, 3])!])/ (Sqrt[(2 Subscript[j, 1])!] Sqrt[(2 Subscript[j, 2])!])) Integrate[Sin[\[Beta]] WignerD[Subscript[m, 1], Subscript[j, 1], Subscript[j, 1], \[Alpha], \[Beta], \[Gamma]] WignerD[Subscript[m, 2], -Subscript[j, 2], Subscript[j, 2], \[Alpha], \[Beta], \[Gamma]] Conjugate[WignerD[-Subscript[m, 3], Subscript[j, 1] - Subscript[j, 2], 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]}]










Standard Form





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MathML Form







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</ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </uplimit> <apply> <int /> <bvar> <ci> &#946; </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <pi /> </uplimit> <apply> <int /> <bvar> <ci> &#945; </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </uplimit> <apply> <times /> <apply> <sin /> <ci> &#946; </ci> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> D </ci> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <ci> &#945; </ci> <ci> &#946; </ci> <ci> &#947; </ci> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> D </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> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> &#945; 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Rule Form





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





2001-12-21





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