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ClebschGordan






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Integral representations > On the real axis > Of the direct function





http://functions.wolfram.com/07.38.07.0004.01









  


  










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)^(Subscript[j, 1] + j - Subscript[m, 1] - m)/ 2^(Subscript[j, 1] + Subscript[j, 2] + 1)) ((Sqrt[(Subscript[j, 1] + Subscript[j, 2] - j)!] Sqrt[(Subscript[j, 1] + Subscript[j, 2] + j + 1)!] Sqrt[2 j + 1])/ (Sqrt[(Subscript[j, 1] + Subscript[m, 1])!] Sqrt[(Subscript[j, 1] - Subscript[m, 1])!] Sqrt[(Subscript[j, 2] + Subscript[m, 2])!] Sqrt[(Subscript[j, 2] - Subscript[m, 2])!])) Integrate[(1 - t^2)^((Subscript[j, 1] + Subscript[j, 2])/2) ((1 - t)/(1 + t))^((Subscript[m, 1] - Subscript[m, 2])/2) WignerD[Subscript[j, 2] - Subscript[j, 1], m, j, ArcCos[t]], {t, -1, 1}] /; \[ScriptCapitalP]\[ScriptH]\[ScriptY]\[ScriptS]\[ScriptI]\ \[ScriptC]\[ScriptA]\[ScriptL]\[ScriptCapitalQ][ {Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {j, m}]










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