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ClebschGordan






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Integral representations > Multiple integral representations > Involving the direct function





http://functions.wolfram.com/07.38.07.0008.01









  


  










Input Form





ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {j, m}] ClebschGordan[{Subscript[j, 1], Subscript[n, 1]}, {Subscript[j, 2], Subscript[n, 2]}, {j, n}] == ((2 j + 1)/(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[m, n, j, \[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]}, {j, m}] && \[ScriptCapitalP]\[ScriptH]\[ScriptY]\[ScriptS]\[ScriptI]\ \[ScriptC]\[ScriptA]\[ScriptL]\[ScriptCapitalQ][ {Subscript[j, 1], Subscript[n, 1]}, {Subscript[j, 2], Subscript[n, 2]}, {j, n}]










Standard Form





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MathML Form







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Rule Form





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





2001-10-29





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