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ClebschGordan




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Generating functions





http://functions.wolfram.com/07.38.11.0001.01









  


  








Input Form





ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {j, m}] == (-1)^(-Subscript[j, 2] + Subscript[j, 1] + m) ((Sqrt[2 j + 1] Sqrt[(Subscript[j, 1] + Subscript[j, 2] + j + 1)!] Sqrt[(Subscript[j, 1] + Subscript[m, 1])!] Sqrt[(Subscript[j, 1] - Subscript[m, 1])!] Sqrt[(Subscript[j, 2] + Subscript[m, 2])!] Sqrt[(Subscript[j, 2] - Subscript[m, 2])!] Sqrt[(j - m)!] Sqrt[(j + m)!])/(Sqrt[(Subscript[j, 1] + Subscript[j, 2] - j)!] Sqrt[(Subscript[j, 2] + j - Subscript[j, 1])!] Sqrt[(j + Subscript[j, 1] - Subscript[j, 2])!])) SeriesTerm[E^((-Subscript[x, 1]) y + x Subscript[y, 1] + Subscript[x, 1] z - Subscript[y, 1] z - x Subscript[z, 1] + y Subscript[z, 1]), {x, 0, Subscript[j, 1] + Subscript[m, 1]}, {Subscript[x, 1], 0, Subscript[j, 1] - Subscript[m, 1]}, {y, 0, Subscript[j, 2] + Subscript[m, 2]}, {Subscript[y, 1], 0, Subscript[j, 2] - Subscript[m, 2]}, {z, 0, j - m}, {Subscript[z, 1], 0, j + m}] /; \[ScriptCapitalP]\[ScriptH]\[ScriptY]\ \[ScriptS]\[ScriptI]\[ScriptC]\[ScriptA]\[ScriptL]\[ScriptCapitalQ][ {Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {j, m}]








Standard Form





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MathML Form







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</mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> j </mi> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> j </mi> <mo> + </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> - </mo> <mi> j </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mi> j </mi> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> j </mi> <mo> + </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> [ </mo> <mrow> <msup> <mi> x </mi> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mrow> </msup> <mo> , </mo> <mtext> </mtext> <msubsup> <mi> x </mi> <mn> 1 </mn> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mrow> </msubsup> <mo> , </mo> <msup> <mi> y </mi> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> </msup> <mo> , </mo> <msubsup> <mi> y </mi> <mn> 1 </mn> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> </msubsup> <mo> , </mo> <msup> <mi> z </mi> <mrow> <mi> j </mi> <mo> - </mo> <mi> m </mi> </mrow> </msup> <mo> , </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mrow> <mi> j </mi> <mo> + </mo> <mi> m </mi> </mrow> </msubsup> </mrow> <mo> ] </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <msub> <mi> x </mi> <mn> 1 </mn> </msub> </mrow> <mo> - </mo> <mrow> <msub> <mi> y </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mi> y </mi> <mo> &#8290; </mo> <msub> <mi> x </mi> <mn> 1 </mn> </msub> </mrow> <mo> - </mo> <msub> <mi> xz </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mrow> <mi> x </mi> <mo> &#8290; </mo> <msub> <mi> y </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mi> y </mi> <mo> &#8290; </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> &#119979;&#119997;&#120014;&#120008;&#119998;&#119992;&#119990;&#8467;&#119980; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <mi> j </mi> <mo> , </mo> <mi> m </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29