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http://functions.wolfram.com/07.39.03.0036.01
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ThreeJSymbol[{Subscript[j, 1], Subscript[j, 1]},
{Subscript[j, 2], -Subscript[j, 2]},
{Subscript[j, 1] - Subscript[j, 2] + 1, -Subscript[j, 1] +
Subscript[j, 2]}] == (-1)^(-2 Subscript[j, 1] + 2 Subscript[j, 2])
(Sqrt[Subscript[j, 2]]/(Sqrt[Subscript[j, 1] + 1]
Sqrt[2 Subscript[j, 1] + 1])) /; Element[2 Subscript[j, 1], Integers] &&
Subscript[j, 1] > 0 && Element[2 Subscript[j, 2], Integers] &&
Subscript[j, 2] > 0 && Subscript[j, 1] >= Subscript[j, 2]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", RowBox[List["-", SubscriptBox["j", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "2"], "+", "1"]], ",", RowBox[List[RowBox[List["-", SubscriptBox["j", "1"]]], "+", SubscriptBox["j", "2"]]]]], "}"]]]], "]"]], " ", "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], SubscriptBox["j", "1"]]], "+", RowBox[List["2", SubscriptBox["j", "2"]]]]]], FractionBox[SqrtBox[SubscriptBox["j", "2"]], RowBox[List[SqrtBox[RowBox[List[SubscriptBox["j", "1"], "+", "1"]]], SqrtBox[RowBox[List[RowBox[List["2", SubscriptBox["j", "1"]]], "+", "1"]]]]]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["2", SubscriptBox["j", "1"]]], "\[Element]", "Integers"]], "\[And]", RowBox[List[SubscriptBox["j", "1"], ">", "0"]], "\[And]", RowBox[List[RowBox[List["2", SubscriptBox["j", "2"]]], "\[Element]", "Integers"]], "\[And]", RowBox[List[SubscriptBox["j", "2"], ">", "0"]], "\[And]", RowBox[List[SubscriptBox["j", "1"], "\[GreaterEqual]", SubscriptBox["j", "2"]]]]]]]]]
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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> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mtd> <mtd> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> </mtd> </mtr> </mtable> <mtext>   </mtext> <semantics> <mo> ) </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[")", Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> </mrow> <mo> ⩵ </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> </mrow> </msup> <mo> ⁢ </mo> <mfrac> <msqrt> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </msqrt> <mrow> <msqrt> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> ≥ </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </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> j </ci> <cn type='integer'> 1 </cn> </apply> </list> <list> <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'> 2 </cn> </apply> </apply> </list> <list> <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> <cn type='integer'> 1 </cn> </apply> <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'> 1 </cn> </apply> </apply> </apply> </list> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </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'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> <apply> <in /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> <apply> <geq /> <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> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", RowBox[List["-", SubscriptBox["j", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "2"], "+", "1"]], ",", RowBox[List[RowBox[List["-", SubscriptBox["j", "1"]]], "+", SubscriptBox["j", "2"]]]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SubscriptBox["j", "1"]]], "+", RowBox[List["2", " ", SubscriptBox["j", "2"]]]]]], " ", SqrtBox[SubscriptBox["j", "2"]]]], RowBox[List[SqrtBox[RowBox[List[SubscriptBox["j", "1"], "+", "1"]]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", SubscriptBox["j", "1"]]], "+", "1"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["2", " ", SubscriptBox["j", "1"]]], "\[Element]", "Integers"]], "&&", RowBox[List[SubscriptBox["j", "1"], ">", "0"]], "&&", RowBox[List[RowBox[List["2", " ", SubscriptBox["j", "2"]]], "\[Element]", "Integers"]], "&&", RowBox[List[SubscriptBox["j", "2"], ">", "0"]], "&&", RowBox[List[SubscriptBox["j", "1"], "\[GreaterEqual]", SubscriptBox["j", "2"]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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