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ClebschGordan




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Identities > Functional identities > Involving two Clebsch Gordan coefficients





http://functions.wolfram.com/07.38.17.0062.01









  


  








Input Form





ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {j, m}] == (Sqrt[1 + 2 j] ClebschGordan[{(1/2) (-1 - j + Subscript[j, 2] + Subscript[m, 1]), (1/2) (1 + j + Subscript[j, 2] - m - Subscript[m, 2])}, {Subscript[j, 1], -1 - j - Subscript[j, 2]}, {(1/2) (-1 + j - Subscript[j, 2] + Subscript[m, 1]), (1/2) (-1 - j - Subscript[j, 2] - m - Subscript[m, 2])}] Sqrt[(Subscript[j, 1] - Subscript[j, 2] - j - 1)!] Sqrt[(j - Subscript[j, 1] + Subscript[j, 2])!] Sqrt[(j - m)!] Sqrt[(m - j - 1)!])/(Sqrt[(Subscript[j, 1] - Subscript[m, 1])!] Sqrt[(Subscript[m, 1] - Subscript[j, 1])!] Sqrt[(-Subscript[j, 2] - Subscript[m, 2] - 1)!] Sqrt[(Subscript[j, 2] + Subscript[m, 2])!] Sqrt[(j - Subscript[j, 2] + Subscript[m, 1] - 1)!])








Standard Form





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MathML Form







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2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <factorial /> <apply> <plus /> <ci> j </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29