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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/07.38.07.0003.01









  


  










Input Form





ClebschGordan[{Subscript[j, 1], 0}, {Subscript[j, 2], 0}, {j, 0}] == ((-1)^(Subscript[j, 1] - j)/2^(Subscript[j, 1] + Subscript[j, 2] + j + 1)) ((Sqrt[(Subscript[j, 1] - Subscript[j, 2] + j)!] Sqrt[(Subscript[j, 1] + Subscript[j, 2] - j)!] Sqrt[(Subscript[j, 1] + Subscript[j, 2] + j + 1)!] Sqrt[2 j + 1])/ (Subscript[j, 1]! Subscript[j, 2]! j! Sqrt[(-Subscript[j, 1] + Subscript[j, 2] + j)!])) Integrate[(1 - t^2)^Subscript[j, 2] D[(1 - t^2)^j, {t, -Subscript[j, 1] + Subscript[j, 2] + j}], {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