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ClebschGordan






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Identities > Functional identities > Arguments j1, j2, j changing by 1





http://functions.wolfram.com/07.38.17.0028.01









  


  










Input Form





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










Standard Form





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MathML Form







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