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ClebschGordan




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Representations through more general functions > Through hypergeometric functions > Involving pFq





http://functions.wolfram.com/07.38.26.0002.01









  


  








Input Form





ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {j, m}] == KroneckerDelta[m, Subscript[m, 1] + Subscript[m, 2]] ((Sqrt[(Subscript[j, 1] - Subscript[j, 2] + j)!] 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)!])) ((Sqrt[(Subscript[j, 1] + Subscript[m, 1])!] Sqrt[(Subscript[j, 2] - Subscript[m, 2])!] Sqrt[(j + m)!] Sqrt[(j - m)!] Sqrt[2 j + 1])/((-Subscript[j, 2] + j + Subscript[m, 1])! (-Subscript[j, 1] + j - Subscript[m, 2])! Sqrt[(Subscript[j, 1] - Subscript[m, 1])!] Sqrt[(Subscript[j, 2] + Subscript[m, 2])!])) HypergeometricPFQ[{-Subscript[j, 1] - Subscript[j, 2] + j, -Subscript[j, 1] + Subscript[m, 1], -Subscript[j, 2] - Subscript[m, 2]}, {-Subscript[j, 1] + j - Subscript[m, 2] + 1, -Subscript[j, 2] + j + Subscript[m, 1] + 1}, 1] /; \[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> <mn> 2 </mn> <mo> &#8290; </mo> <mi> j </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mi> j </mi> <mo> + </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mi> j </mi> <mo> - </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <msqrt> <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> </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> </mrow> </mfrac> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 3 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mi> j </mi> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> - </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> </mrow> <mo> ; </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mi> j </mi> <mo> - </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mi> j </mi> <mo> + </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ; </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;3&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;2&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[RowBox[List[&quot;-&quot;, SubscriptBox[&quot;j&quot;, &quot;1&quot;]]], &quot;-&quot;, SubscriptBox[&quot;j&quot;, &quot;2&quot;], &quot;+&quot;, &quot;j&quot;]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[RowBox[List[&quot;-&quot;, SubscriptBox[&quot;j&quot;, &quot;1&quot;]]], &quot;+&quot;, SubscriptBox[&quot;m&quot;, &quot;1&quot;]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[RowBox[List[&quot;-&quot;, SubscriptBox[&quot;j&quot;, &quot;2&quot;]]], &quot;-&quot;, SubscriptBox[&quot;m&quot;, &quot;2&quot;]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[RowBox[List[RowBox[List[&quot;-&quot;, SubscriptBox[&quot;j&quot;, &quot;1&quot;]]], &quot;+&quot;, &quot;j&quot;, &quot;-&quot;, SubscriptBox[&quot;m&quot;, &quot;2&quot;], &quot;+&quot;, &quot;1&quot;]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[RowBox[List[&quot;-&quot;, SubscriptBox[&quot;j&quot;, &quot;2&quot;]]], &quot;+&quot;, &quot;j&quot;, &quot;+&quot;, SubscriptBox[&quot;m&quot;, &quot;1&quot;], &quot;+&quot;, &quot;1&quot;]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[&quot;1&quot;, HypergeometricPFQ, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> </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