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ClebschGordan






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Summation > Finite summation > Involving three Clebsch Gordan coefficients





http://functions.wolfram.com/07.38.23.0019.01









  


  










Input Form





Sum[(-1)^(Subscript[j, 2] + Subscript[m, 2]) ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 3], Subscript[m, 3]}] ClebschGordan[{Subscript[j, 2], -Subscript[m, 2]}, {Subscript[j, 4], Subscript[m, 4]}, {Subscript[j, 6], Subscript[m, 6]}] ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 5], Subscript[m, 5]}, {Subscript[j, 6], Subscript[m, 6]}], {Subscript[m, 1], -Subscript[j, 1], Subscript[j, 1]}, {Subscript[m, 2], -Subscript[j, 2], Subscript[j, 2]}, {Subscript[m, 6], -Subscript[j, 6], Subscript[j, 6]}] == (-1)^(Subscript[j, 2] + Subscript[j, 3] + Subscript[j, 5] + Subscript[j, 6]) ((Sqrt[2 Subscript[j, 3] + 1] (2 Subscript[j, 6] + 1))/ Sqrt[2 Subscript[j, 4] + 1]) ClebschGordan[ {Subscript[j, 3], Subscript[m, 3]}, {Subscript[j, 5], Subscript[m, 5]}, {Subscript[j, 4], Subscript[m, 4]}] SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 4], Subscript[j, 5], Subscript[j, 6]}]










Standard Form





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MathML Form







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</ci> <cn type='integer'> 3 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 5 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> </list> </apply> <apply> <ci> SixJSymbol </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </list> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-12-21





© 1998- Wolfram Research, Inc.