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ClebschGordan




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.38.17.0038.01









  


  








Input Form





ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2] - 1, Subscript[m, 2]}, {j, m}] == ((Sqrt[j - m] Sqrt[j - m - 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] Sqrt[Subscript[j, 1] + Subscript[j, 2] - j + 1])/ (2 j Sqrt[2 j - 1] Sqrt[2 j + 1] Sqrt[Subscript[j, 2] + Subscript[m, 2]] Sqrt[Subscript[j, 2] + Subscript[m, 2] + 1])) ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2] + 1}, {j - 1, m + 1}] - ((Sqrt[j - m] Sqrt[j + m + 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] Sqrt[Subscript[j, 1] + Subscript[j, 2] + j + 1])/ (2 j (j + 1) Sqrt[Subscript[j, 2] + Subscript[m, 2]] Sqrt[Subscript[j, 2] + Subscript[m, 2] + 1])) ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2] + 1}, {j, m + 1}] + ((Sqrt[j + m + 1] Sqrt[j + m + 2] 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 (j + 1) Sqrt[2 j + 1] Sqrt[2 j + 3] Sqrt[Subscript[j, 2] + Subscript[m, 2]] Sqrt[Subscript[j, 2] + Subscript[m, 2] + 1])) ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2] + 1}, {j + 1, m + 1}]








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