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SixJSymbol




Mathematica Notation

Traditional Notation









Hypergeometric Functions > SixJSymbol[{j1,j2,j3},{j4,j5,j6}] > Identities > Functional identities > Arguments changing by 1/2





http://functions.wolfram.com/07.40.17.0005.01









  


  








Input Form





SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 4], Subscript[j, 5], Subscript[j, 6]}] == (-((Sqrt[Subscript[j, 1] + Subscript[j, 5] + Subscript[j, 6] + 1] Sqrt[Subscript[j, 1] - Subscript[j, 5] + Subscript[j, 6]] Sqrt[Subscript[j, 2] + Subscript[j, 4] + Subscript[j, 6] + 1] Sqrt[-Subscript[j, 2] + Subscript[j, 4] + Subscript[j, 6]] Sqrt[Subscript[j, 3] + Subscript[j, 4] + Subscript[j, 5] + 1] Sqrt[Subscript[j, 3] + Subscript[j, 4] - Subscript[j, 5]])/ ((2 Subscript[j, 4] + 1) (2 Subscript[j, 6] + 1) Sqrt[Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 3] + 1] Sqrt[Subscript[j, 1] - Subscript[j, 2] + Subscript[j, 3]]))) SixJSymbol[{Subscript[j, 1] - 1/2, Subscript[j, 2], Subscript[j, 3] - 1/2}, {Subscript[j, 4] - 1/2, Subscript[j, 5], Subscript[j, 6] - 1/2}] - ((Sqrt[-Subscript[j, 1] + Subscript[j, 5] + Subscript[j, 6] + 1] Sqrt[Subscript[j, 1] + Subscript[j, 5] - Subscript[j, 6]] Sqrt[Subscript[j, 2] - Subscript[j, 4] + Subscript[j, 6] + 1] Sqrt[Subscript[j, 2] + Subscript[j, 4] - Subscript[j, 6]] Sqrt[Subscript[j, 3] + Subscript[j, 4] + Subscript[j, 5] + 1] Sqrt[Subscript[j, 3] + Subscript[j, 4] - Subscript[j, 5]])/ ((2 Subscript[j, 4] + 1) (2 Subscript[j, 6] + 1) Sqrt[Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 3] + 1] Sqrt[Subscript[j, 1] - Subscript[j, 2] + Subscript[j, 3]])) SixJSymbol[{Subscript[j, 1] - 1/2, Subscript[j, 2], Subscript[j, 3] - 1/2}, {Subscript[j, 4] - 1/2, Subscript[j, 5], Subscript[j, 6] + 1/2}] - ((Sqrt[Subscript[j, 1] + Subscript[j, 5] + Subscript[j, 6] + 1] Sqrt[Subscript[j, 1] - Subscript[j, 5] + Subscript[j, 6]] Sqrt[Subscript[j, 2] + Subscript[j, 4] - Subscript[j, 6] + 1] Sqrt[Subscript[j, 2] - Subscript[j, 4] + Subscript[j, 6]] Sqrt[-Subscript[j, 3] + Subscript[j, 4] + Subscript[j, 5] + 1] Sqrt[Subscript[j, 3] - Subscript[j, 4] + Subscript[j, 5]])/ ((2 Subscript[j, 4] + 1) (2 Subscript[j, 6] + 1) Sqrt[Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 3] + 1] Sqrt[Subscript[j, 1] - Subscript[j, 2] + Subscript[j, 3]])) SixJSymbol[{Subscript[j, 1] - 1/2, Subscript[j, 2], Subscript[j, 3] - 1/2}, {Subscript[j, 4] + 1/2, Subscript[j, 5], Subscript[j, 6] - 1/2}] + ((Sqrt[-Subscript[j, 1] + Subscript[j, 5] + Subscript[j, 6] + 1] Sqrt[Subscript[j, 1] + Subscript[j, 5] - Subscript[j, 6]] Sqrt[Subscript[j, 2] + Subscript[j, 4] + Subscript[j, 6] + 2] Sqrt[-Subscript[j, 2] + Subscript[j, 4] + Subscript[j, 6] + 1] Sqrt[-Subscript[j, 3] + Subscript[j, 4] + Subscript[j, 5] + 1] Sqrt[Subscript[j, 3] - Subscript[j, 4] + Subscript[j, 5]])/ ((2 Subscript[j, 4] + 1) (2 Subscript[j, 6] + 1) Sqrt[Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 3] + 1] Sqrt[Subscript[j, 1] - Subscript[j, 2] + Subscript[j, 3]])) SixJSymbol[{Subscript[j, 1] - 1/2, Subscript[j, 2], Subscript[j, 3] - 1/2}, {Subscript[j, 4] + 1/2, Subscript[j, 5], Subscript[j, 6] + 1/2}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "2"], ",", SubscriptBox["j", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox["j", "5"], ",", SubscriptBox["j", "6"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "5"], "+", SubscriptBox["j", "6"], "+", "1"]]], SqrtBox[RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "5"], "+", SubscriptBox["j", "6"]]]], SqrtBox[RowBox[List[SubscriptBox["j", "2"], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "6"], "+", "1"]]], SqrtBox[RowBox[List[RowBox[List["-", SubscriptBox["j", "2"]]], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "6"]]]], SqrtBox[RowBox[List[SubscriptBox["j", "3"], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "5"], "+", "1"]]], SqrtBox[RowBox[List[SubscriptBox["j", "3"], "+", SubscriptBox["j", "4"], "-", SubscriptBox["j", "5"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", SubscriptBox["j", "4"]]], "+", "1"]], ")"]], RowBox[List["(", RowBox[List[RowBox[List["2", SubscriptBox["j", "6"]]], "+", "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"]]]]]], ")"]]]]]], RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["j", "1"], "-", FractionBox["1", "2"]]], ",", SubscriptBox["j", "2"], ",", RowBox[List[SubscriptBox["j", "3"], "-", FractionBox["1", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["j", "4"], "-", FractionBox["1", "2"]]], ",", SubscriptBox["j", "5"], ",", RowBox[List[SubscriptBox["j", "6"], "-", FractionBox["1", "2"]]]]], "}"]]]], "]"]]]], "-", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SubscriptBox["j", "1"]]], "+", SubscriptBox["j", "5"], "+", SubscriptBox["j", "6"], "+", "1"]]], SqrtBox[RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "5"], "-", SubscriptBox["j", "6"]]]], SqrtBox[RowBox[List[SubscriptBox["j", "2"], "-", SubscriptBox["j", "4"], "+", SubscriptBox["j", "6"], "+", "1"]]], SqrtBox[RowBox[List[SubscriptBox["j", "2"], "+", SubscriptBox["j", "4"], "-", SubscriptBox["j", "6"]]]], SqrtBox[RowBox[List[SubscriptBox["j", "3"], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "5"], "+", "1"]]], SqrtBox[RowBox[List[SubscriptBox["j", "3"], "+", SubscriptBox["j", "4"], "-", SubscriptBox["j", "5"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", SubscriptBox["j", "4"]]], "+", "1"]], ")"]], RowBox[List["(", RowBox[List[RowBox[List["2", SubscriptBox["j", "6"]]], "+", "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"]]]]]], ")"]]]], RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["j", "1"], "-", FractionBox["1", "2"]]], ",", SubscriptBox["j", "2"], ",", RowBox[List[SubscriptBox["j", "3"], "-", FractionBox["1", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["j", "4"], "-", FractionBox["1", "2"]]], ",", SubscriptBox["j", "5"], ",", RowBox[List[SubscriptBox["j", "6"], "+", FractionBox["1", "2"]]]]], "}"]]]], "]"]]]], "-", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "5"], "+", SubscriptBox["j", "6"], "+", "1"]]], SqrtBox[RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "5"], "+", SubscriptBox["j", "6"]]]], SqrtBox[RowBox[List[SubscriptBox["j", "2"], "+", SubscriptBox["j", "4"], "-", SubscriptBox["j", "6"], "+", "1"]]], SqrtBox[RowBox[List[SubscriptBox["j", "2"], "-", SubscriptBox["j", "4"], "+", SubscriptBox["j", "6"]]]], SqrtBox[RowBox[List[RowBox[List["-", SubscriptBox["j", "3"]]], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "5"], "+", "1"]]], SqrtBox[RowBox[List[SubscriptBox["j", "3"], "-", SubscriptBox["j", "4"], "+", SubscriptBox["j", "5"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", SubscriptBox["j", "4"]]], "+", "1"]], ")"]], RowBox[List["(", RowBox[List[RowBox[List["2", SubscriptBox["j", "6"]]], "+", "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"]]]]]], ")"]]]], RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["j", "1"], "-", FractionBox["1", "2"]]], ",", SubscriptBox["j", "2"], ",", RowBox[List[SubscriptBox["j", "3"], "-", FractionBox["1", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["j", "4"], "+", FractionBox["1", "2"]]], ",", SubscriptBox["j", "5"], ",", RowBox[List[SubscriptBox["j", "6"], "-", FractionBox["1", "2"]]]]], "}"]]]], "]"]]]], "+", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SubscriptBox["j", "1"]]], "+", SubscriptBox["j", "5"], "+", SubscriptBox["j", "6"], "+", "1"]]], SqrtBox[RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "5"], "-", SubscriptBox["j", "6"]]]], SqrtBox[RowBox[List[SubscriptBox["j", "2"], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "6"], "+", "2"]]], SqrtBox[RowBox[List[RowBox[List["-", SubscriptBox["j", "2"]]], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "6"], "+", "1"]]], SqrtBox[RowBox[List[RowBox[List["-", SubscriptBox["j", "3"]]], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "5"], "+", "1"]]], SqrtBox[RowBox[List[SubscriptBox["j", "3"], "-", SubscriptBox["j", "4"], "+", SubscriptBox["j", "5"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", SubscriptBox["j", "4"]]], "+", "1"]], ")"]], RowBox[List["(", RowBox[List[RowBox[List["2", SubscriptBox["j", "6"]]], "+", "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"]]]]]], ")"]]]], RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["j", "1"], "-", FractionBox["1", "2"]]], ",", SubscriptBox["j", "2"], ",", RowBox[List[SubscriptBox["j", "3"], "-", FractionBox["1", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["j", "4"], "+", FractionBox["1", "2"]]], ",", SubscriptBox["j", "5"], ",", RowBox[List[SubscriptBox["j", "6"], "+", FractionBox["1", "2"]]]]], "}"]]]], "]"]]]]]]]]]]








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]]], SixJSymbol] </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> j </mi> <mn> 4 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mtd> </mtr> </mtable> <mtext> &#8287; </mtext> <semantics> <mo> } </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;}&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], SixJSymbol] </annotation> </semantics> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </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> 5 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <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> </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]]], SixJSymbol] </annotation> </semantics> <mtext> &#8287; </mtext> <mtable> <mtr> <mtd> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> <mtd> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> <mtd> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mtd> <mtd> <mrow> <msub> <mi> j </mi> <mn> 6 </mn> </msub> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> </mtr> </mtable> <mtext> &#8287; </mtext> <semantics> <mo> } </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;}&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], SixJSymbol] </annotation> </semantics> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </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> 5 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </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> j </mi> <mn> 4 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <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> </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]]], SixJSymbol] </annotation> </semantics> <mtext> &#8287; </mtext> <mtable> <mtr> <mtd> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> <mtd> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> <mtd> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mtd> <mtd> <mrow> <msub> <mi> j </mi> <mn> 6 </mn> </msub> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> </mtr> </mtable> <mtext> &#8287; </mtext> <semantics> <mo> } </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;}&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], SixJSymbol] </annotation> </semantics> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </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> 5 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 6 </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> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <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> </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]]], SixJSymbol] </annotation> </semantics> <mtext> &#8287; </mtext> <mtable> <mtr> <mtd> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> <mtd> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> <mtd> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mtd> <mtd> <mrow> <msub> <mi> j </mi> <mn> 6 </mn> </msub> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> </mtr> </mtable> <mtext> &#8287; </mtext> <semantics> <mo> } </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;}&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], SixJSymbol] </annotation> </semantics> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </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> 5 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <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> </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]]], SixJSymbol] </annotation> </semantics> <mtext> &#8287; </mtext> <mtable> <mtr> <mtd> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> <mtd> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> <mtd> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mtd> <mtd> <mrow> <msub> <mi> j </mi> <mn> 6 </mn> </msub> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> </mtr> </mtable> <mtext> &#8287; </mtext> <semantics> <mo> } </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;}&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], SixJSymbol] </annotation> </semantics> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> SixJSymbol </ci> <list> <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> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </list> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <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'> 5 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </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'> 5 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </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> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </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'> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </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'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </apply> <cn type='integer'> 1 </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'> 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> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> SixJSymbol </ci> <list> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </list> <list> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </list> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <times /> <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'> 5 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </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'> 5 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </apply> </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> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </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'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </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'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> 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Rule Form





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





2001-12-21