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ThreeJSymbol






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ThreeJSymbol[{j1,m1},{j2,m2},{j3,m3}] > Series representations > Other series representations > Series of binomial coefficients





http://functions.wolfram.com/07.39.06.0003.01









  


  










Input Form





ThreeJSymbol[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 3], Subscript[m, 3]}] == ((-1)^(-Subscript[j, 1] + Subscript[j, 2] + Subscript[m, 3])/ Sqrt[2 Subscript[j, 3] + 1]) KroneckerDelta[Subscript[m, 1] + Subscript[m, 2], -Subscript[m, 3]] ((Sqrt[Binomial[2 Subscript[j, 1], Subscript[j, 1] + Subscript[j, 2] - Subscript[j, 3]]] Sqrt[Binomial[2 Subscript[j, 2], Subscript[j, 1] + Subscript[j, 2] - Subscript[j, 3]]])/ (Sqrt[Binomial[Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 3] + 1, Subscript[j, 1] + Subscript[j, 2] - Subscript[j, 3]]] Sqrt[Binomial[2 Subscript[j, 1], Subscript[j, 1] - Subscript[m, 1]]] Sqrt[Binomial[2 Subscript[j, 2], Subscript[j, 2] - Subscript[m, 2]]] Sqrt[Binomial[2 Subscript[j, 3], Subscript[j, 3] + Subscript[m, 3]]])) Sum[(-1)^k Binomial[Subscript[j, 1] + Subscript[j, 2] - Subscript[j, 3], k] Binomial[Subscript[j, 1] - Subscript[j, 2] + Subscript[j, 3], Subscript[j, 1] - Subscript[m, 1] - k] Binomial[-Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 3], Subscript[j, 2] + Subscript[m, 2] - k], {k, Max[0, Subscript[j, 2] - Subscript[j, 3] - Subscript[m, 1], Subscript[j, 1] - Subscript[j, 3] + Subscript[m, 2]], Min[Subscript[j, 1] + Subscript[j, 2] - Subscript[j, 3], Subscript[j, 1] - Subscript[m, 1], Subscript[j, 2] + Subscript[m, 2]]}] /; \[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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Rule Form





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





2001-10-29





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