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ClebschGordan




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Series representations > Other series representations > Series of binomial coefficients





http://functions.wolfram.com/07.38.06.0003.01









  


  








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]] ((Sqrt[Binomial[2 Subscript[j, 1], Subscript[j, 1] + Subscript[j, 2] - j]] Sqrt[Binomial[2 Subscript[j, 2], Subscript[j, 1] + Subscript[j, 2] - j]])/(Sqrt[Binomial[Subscript[j, 1] + Subscript[j, 2] + j + 1, Subscript[j, 1] + Subscript[j, 2] - j]] 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 j, j - m]])) Sum[(-1)^k Binomial[Subscript[j, 1] + Subscript[j, 2] - j, k] Binomial[Subscript[j, 1] - Subscript[j, 2] + j, Subscript[j, 1] - Subscript[m, 1] - k] Binomial[-Subscript[j, 1] + Subscript[j, 2] + j, Subscript[j, 2] + Subscript[m, 2] - k], {k, Max[0, Subscript[j, 2] - j - Subscript[m, 1], Subscript[j, 1] - j + Subscript[m, 2]], Min[Subscript[j, 1] + Subscript[j, 2] - j, 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]}, {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