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ClebschGordan




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Identities > Functional identities > Arguments m1, m2, m equal to zero





http://functions.wolfram.com/07.38.17.0043.01









  


  








Input Form





ClebschGordan[{Subscript[j, 1] + n, 0}, {Subscript[j, 2] - n, 0}, {j, 0}] == ((((-Subscript[j, 1] + Subscript[j, 2] + j)/2)! ((Subscript[j, 1] - Subscript[j, 2] + j)/2)! Sqrt[(-Subscript[j, 1] + Subscript[j, 2] + j - 2 n)!] Sqrt[(Subscript[j, 1] - Subscript[j, 2] + j + 2 n)!])/ (((-Subscript[j, 1] + Subscript[j, 2] + j)/2 - n)! ((Subscript[j, 1] - Subscript[j, 2] + j)/2 + n)! Sqrt[(-Subscript[j, 1] + Subscript[j, 2] + j)!] Sqrt[(Subscript[j, 1] - Subscript[j, 2] + j)!])) ClebschGordan[{Subscript[j, 1], 0}, {Subscript[j, 2], 0}, {j, 0}] /; Element[n, Integers] && Max[-Subscript[j, 1], (-Subscript[j, 1] + Subscript[j, 2] - j)/2] <= n <= Min[Subscript[j, 2], (-Subscript[j, 1] + Subscript[j, 2] + j)/2] && Element[Subscript[j, 1], Integers] && Subscript[j, 1] >= 0 && Element[Subscript[j, 2], Integers] && Subscript[j, 2] >= 0 && Element[j, Integers] && j >= 0 && Abs[Subscript[j, 1] - Subscript[j, 2]] <= j <= Subscript[j, 1] + Subscript[j, 2]








Standard Form





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MathML Form







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</apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#8469; </ci> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8469; </ci> </apply> <apply> <in /> <ci> j </ci> <ci> &#8469; </ci> </apply> <apply> <leq /> <apply> <abs /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <ci> j </ci> <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> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29