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http://functions.wolfram.com/07.39.17.0015.01
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ThreeJSymbol[{Subscript[j, 1], Subscript[m, 1]},
{Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 3], Subscript[m, 3]}] ==
((Sqrt[(Subscript[j, 1] + Subscript[j, 2] - Subscript[j, 3])!]
Sqrt[(-Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 3])!]
Sqrt[(Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 3] + 1)!]
Sqrt[(-2 n + Subscript[j, 2] + Subscript[m, 2])!]
Sqrt[(Subscript[j, 3] - Subscript[m, 3])!])/
(Sqrt[(Subscript[j, 1] - Subscript[j, 2] + Subscript[j, 3])!]
Sqrt[(Subscript[j, 2] + Subscript[m, 2])!]
Sqrt[(Subscript[j, 3] + Subscript[m, 3])!]))
Sum[(-1)^(-Subscript[j, 3] + k + n) (((2 k + 1) (Subscript[j, 3] + k - n)!
(2 n)! Sqrt[(k - -Subscript[m, 3] + n)!]
Sqrt[(Subscript[j, 1] - Subscript[j, 2] + k + n)!])/
((Subscript[j, 3] - k + n)! (Subscript[j, 3] + k + n + 1)!
(-Subscript[j, 3] + k + n)! Sqrt[(k - Subscript[m, 3] - n)!]
Sqrt[(-Subscript[j, 1] + Subscript[j, 2] + k - n)!]
Sqrt[(Subscript[j, 1] + Subscript[j, 2] - k - n)!]
Sqrt[(Subscript[j, 1] + Subscript[j, 2] + k - n + 1)!]))
ThreeJSymbol[{Subscript[j, 1], Subscript[m, 1]},
{Subscript[j, 2] - n, Subscript[m, 2] - n}, {k, Subscript[m, 3] + n}],
{k, Subscript[j, 3] - n, Subscript[j, 3] + n}] /;
Element[2 n, Integers] && 0 <= n <= (Subscript[j, 2] + Subscript[m, 2])/2 &&
\[ScriptCapitalP]\[ScriptH]\[ScriptY]\[ScriptS]\[ScriptI]\[ScriptC]\
\[ScriptA]\[ScriptL]\[ScriptCapitalQ][{Subscript[j, 1], Subscript[m, 1]},
{Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 3], Subscript[m, 3]}]
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Cell[BoxData[RowBox[List[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[SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "-", SubscriptBox["j", "3"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SubscriptBox["j", "1"]]], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"], "+", "1"]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "n"]], "+", SubscriptBox["j", "2"], "+", SubscriptBox["m", "2"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "3"], "-", SubscriptBox["m", "3"]]], ")"]], "!"]]]]], ")"]], "/", RowBox[List["(", RowBox[List[SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "2"], "+", SubscriptBox["m", "2"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "3"], "+", SubscriptBox["m", "3"]]], ")"]], "!"]]]]], ")"]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List[SubscriptBox["j", "3"], "-", "n"]]]], RowBox[List[SubscriptBox["j", "3"], "+", "n"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", SubscriptBox["j", "3"]]], "+", "k", "+", "n"]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", "k"]], "+", "1"]], ")"]], RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "3"], "+", "k", "-", "n"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["2", " ", "n"]], ")"]], "!"]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["k", "-", RowBox[List["-", SubscriptBox["m", "3"]]], "+", "n"]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "2"], "+", "k", "+", "n"]], ")"]], "!"]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "3"], "-", "k", "+", "n"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "3"], "+", "k", "+", "n", "+", "1"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SubscriptBox["j", "3"]]], "+", "k", "+", "n"]], ")"]], "!"]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["k", "-", SubscriptBox["m", "3"], "-", "n"]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SubscriptBox["j", "1"]]], "+", SubscriptBox["j", "2"], "+", "k", "-", "n"]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "-", "k", "-", "n"]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "+", "k", "-", "n", "+", "1"]], ")"]], "!"]]]]], ")"]]]], RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["j", "2"], "-", "n"]], ",", RowBox[List[SubscriptBox["m", "2"], "-", "n"]]]], "}"]], ",", RowBox[List["{", RowBox[List["k", ",", RowBox[List[SubscriptBox["m", "3"], "+", "n"]]]], "}"]]]], "]"]]]]]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["2", "n"]], "\[Element]", "Integers"]], "\[And]", RowBox[List["0", "\[LessEqual]", "n", "\[LessEqual]", FractionBox[RowBox[List[SubscriptBox["j", "2"], "+", SubscriptBox["m", "2"]]], "2"]]], "\[And]", RowBox[List["\[ScriptCapitalP]\[ScriptH]\[ScriptY]\[ScriptS]\[ScriptI]\[ScriptC]\[ScriptA]\[ScriptL]\[ScriptCapitalQ]", "[", 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"]]], "}"]]]], "]"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <semantics> <mo> ( </mo> <annotation encoding='Mathematica'> TagBox[StyleBox["(", Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> <mtext>   </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>   </mtext> <semantics> <mo> ) </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[")", Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <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> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <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> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> ⁢ </mo> <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> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> + </mo> <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> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 3 </mn> </msub> </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> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> ⁢ </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> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> m </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> - </mo> <mi> n </mi> </mrow> </mrow> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mi> n </mi> </mrow> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mi> k </mi> <mo> + </mo> <mi> n </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <mrow> <mo> - </mo> <msub> <mi> m </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> ⁢ </mo> <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> k </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mi> k </mi> <mo> + </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mi> k </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <msub> <mi> m </mi> <mn> 3 </mn> </msub> <mo> - </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <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> k </mi> <mo> - </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> ⁢ </mo> <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> k </mi> <mo> - </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> ⁢ </mo> <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> k </mi> <mo> - </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <semantics> <mo> ( </mo> <annotation encoding='Mathematica'> TagBox[StyleBox["(", Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> <mtext>   </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> <mi> n </mi> </mrow> </mtd> <mtd> <mi> k </mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mtd> <mtd> <mrow> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> - </mo> <mi> n </mi> </mrow> </mtd> <mtd> <mrow> <mi> n </mi> <mo> + </mo> <msub> <mi> m </mi> <mn> 3 </mn> </msub> </mrow> </mtd> </mtr> </mtable> <mtext>   </mtext> <semantics> <mo> ) </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[")", Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> ∈ </mo> <mi> ℕ </mi> </mrow> <mo> ∧ </mo> <mrow> <mi> n </mi> <mo> ≤ </mo> <mfrac> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> ∧ </mo> <mrow> <mi> 𝒫𝒽𝓎𝓈𝒾𝒸𝒶ℓ𝒬 </mi> <mo> ⁡ </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> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> , </mo> <msub> <mi> m </mi> <mn> 3 </mn> </msub> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <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> <times /> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <factorial /> <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> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <factorial /> <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> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <factorial /> <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 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