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ThreeJSymbol






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ThreeJSymbol[{j1,m1},{j2,m2},{j3,m3}] > Identities > Recurrence identities > Consecutive neighbors





http://functions.wolfram.com/07.39.17.0012.01









  


  










Input Form





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










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["m", "3"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", SubscriptBox["j", "2"]]], "+", "3"]], ")"]], RowBox[List["(", RowBox[List[RowBox[List["2", " ", SubscriptBox["m", "1"], RowBox[List["(", RowBox[List[SubscriptBox["j", "2"], "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["j", "2"], "+", "2"]], ")"]]]], "+", RowBox[List[SubscriptBox["m", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "2"], "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["j", "2"], "+", "2"]], ")"]]]], "+", RowBox[List[SubscriptBox["j", "1"], RowBox[List["(", RowBox[List[SubscriptBox["j", "1"], "+", "1"]], ")"]]]], "-", RowBox[List[SubscriptBox["j", "3"], " ", RowBox[List["(", RowBox[List[SubscriptBox["j", "3"], "+", "1"]], ")"]]]]]], ")"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "2"], "+", "2"]], ")"]], SqrtBox[RowBox[List[SubscriptBox["j", "2"], "-", SubscriptBox["m", "2"], "+", "1"]]], SqrtBox[RowBox[List[SubscriptBox["j", "2"], "+", SubscriptBox["m", "2"], "+", "1"]]], " ", SqrtBox[RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"]]]], " ", SqrtBox[RowBox[List[RowBox[List["-", SubscriptBox["j", "1"]]], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"], "+", "1"]]], " ", SqrtBox[RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "-", SubscriptBox["j", "3"], "+", "1"]]], " ", SqrtBox[RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"], "+", "2"]]]]], ")"]]]]]], RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["j", "2"], "+", "1"]], ",", SubscriptBox["m", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["m", "3"]]], "}"]]]], "]"]]]], "-", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "2"], "+", "1"]], ")"]], SqrtBox[RowBox[List[SubscriptBox["j", "2"], "-", SubscriptBox["m", "2"], "+", "2"]]], SqrtBox[RowBox[List[SubscriptBox["j", "2"], "+", SubscriptBox["m", "2"], "+", "2"]]], SqrtBox[RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"], "-", "1"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", SubscriptBox["j", "1"]]], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"], "+", "2"]]], " ", SqrtBox[RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "-", SubscriptBox["j", "3"], "+", "2"]]], " ", SqrtBox[RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"], "+", "3"]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "2"], "+", "2"]], ")"]], SqrtBox[RowBox[List[SubscriptBox["j", "2"], "-", SubscriptBox["m", "2"], "+", "1"]]], SqrtBox[RowBox[List[SubscriptBox["j", "2"], "+", SubscriptBox["m", "2"], "+", "1"]]], SqrtBox[RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"]]]], " ", SqrtBox[RowBox[List[RowBox[List["-", SubscriptBox["j", "1"]]], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"], "+", "1"]]], " ", SqrtBox[RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "-", SubscriptBox["j", "3"], "+", "1"]]], " ", SqrtBox[RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"], "+", "2"]]]]], ")"]]]], " ", RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["j", "2"], "+", "2"]], ",", SubscriptBox["m", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["m", "3"]]], "}"]]]], "]"]]]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mo> ( </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;(&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> <mtext> &#8287; </mtext> <mtable> <mtr> <mtd> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mtd> <mtd> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <msub> <mi> m </mi> <mn> 3 </mn> </msub> </mtd> </mtr> </mtable> <mtext> &#8287; </mtext> <semantics> <mo> ) </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;)&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <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> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mo> ( </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;(&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> <mtext> &#8287; </mtext> <mtable> <mtr> <mtd> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mtd> <mtd> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </mtd> <mtd> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mtd> <mtd> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <msub> <mi> m </mi> <mn> 3 </mn> </msub> </mtd> </mtr> </mtable> <mtext> &#8287; </mtext> <semantics> <mo> ) </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;)&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <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> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 3 </mn> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <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> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mo> ( </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;(&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> <mtext> &#8287; </mtext> <mtable> <mtr> <mtd> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mtd> <mtd> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> </mtd> <mtd> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mtd> <mtd> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <msub> <mi> m </mi> <mn> 3 </mn> </msub> </mtd> </mtr> </mtable> <mtext> &#8287; </mtext> <semantics> <mo> ) </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;)&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> ThreeJSymbol </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <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 /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </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'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </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> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </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> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </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> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> ThreeJSymbol </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </list> <list> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </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> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </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> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> 2 </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> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </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'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </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> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </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> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </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> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> ThreeJSymbol </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </list> <list> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-12-21