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ThreeJSymbol




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ThreeJSymbol[{j1,m1},{j2,m2},{j3,m3}] > Primary definition





http://functions.wolfram.com/07.39.02.0004.01









  


  








Input Form





\[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]}] == \[ScriptCapitalT]\[ScriptR]\[ScriptI]\[ScriptA]\[ScriptN]\[ScriptG]\ \[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\[ScriptCapitalQ][Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]] && Element[Subscript[j, 1] - Subscript[m, 1], Integers] && Element[Subscript[j, 2] - Subscript[m, 2], Integers] && Element[Subscript[j, 3] - Subscript[m, 3], Integers] && -Subscript[j, 1] <= Subscript[m, 1] <= Subscript[j, 1] && -Subscript[j, 2] <= Subscript[m, 2] <= Subscript[j, 2] && -Subscript[j, 3] <= Subscript[m, 3] <= Subscript[j, 3]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[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"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List["\[ScriptCapitalT]\[ScriptR]\[ScriptI]\[ScriptA]\[ScriptN]\[ScriptG]\[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\[ScriptCapitalQ]", "[", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "2"], ",", SubscriptBox["j", "3"]]], "]"]]]], "\[And]", RowBox[List[RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["m", "1"]]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List[SubscriptBox["j", "2"], "-", SubscriptBox["m", "2"]]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List[SubscriptBox["j", "3"], "-", SubscriptBox["m", "3"]]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["-", SubscriptBox["j", "1"]]], "\[LessEqual]", SubscriptBox["m", "1"], "\[LessEqual]", SubscriptBox["j", "1"]]], "\[And]", RowBox[List[RowBox[List["-", SubscriptBox["j", "2"]]], "\[LessEqual]", SubscriptBox["m", "2"], "\[LessEqual]", SubscriptBox["j", "2"]]], "\[And]", RowBox[List[RowBox[List["-", SubscriptBox["j", "3"]]], "\[LessEqual]", SubscriptBox["m", "3"], "\[LessEqual]", SubscriptBox["j", "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> <mrow> <mrow> <mi> &#119983;&#120007;&#119998;&#119990;&#120003;&#8458;&#120010;&#8467;&#119990;&#120007;&#119980; </mi> <mo> &#8289; </mo> <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> &#10869; </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> </mrow> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <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> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &#8804; </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> &#8804; </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> <and /> <apply> <in /> <apply> <eq /> <apply> <ci> &#119983;&#120007;&#119998;&#119990;&#120003;&#8458;&#120010;&#8467;&#119990;&#120007;&#119980; </ci> <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> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <ci> &#8469; </ci> </apply> <apply> <in /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> &#8469; </ci> </apply> <apply> <in /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </apply> <ci> &#8469; </ci> </apply> <apply> <in /> <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> </apply> <ci> &#8469; </ci> </apply> <apply> <leq /> <apply> <abs /> <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> </apply> <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'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List[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"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List["\[ScriptCapitalT]\[ScriptR]\[ScriptI]\[ScriptA]\[ScriptN]\[ScriptG]\[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\[ScriptCapitalQ]", "[", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "2"], ",", SubscriptBox["j", "3"]]], "]"]]]], "&&", RowBox[List[RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["m", "1"]]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List[SubscriptBox["j", "2"], "-", SubscriptBox["m", "2"]]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List[SubscriptBox["j", "3"], "-", SubscriptBox["m", "3"]]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", SubscriptBox["j", "1"]]], "\[LessEqual]", SubscriptBox["m", "1"], "\[LessEqual]", SubscriptBox["j", "1"]]], "&&", RowBox[List[RowBox[List["-", SubscriptBox["j", "2"]]], "\[LessEqual]", SubscriptBox["m", "2"], "\[LessEqual]", SubscriptBox["j", "2"]]], "&&", RowBox[List[RowBox[List["-", SubscriptBox["j", "3"]]], "\[LessEqual]", SubscriptBox["m", "3"], "\[LessEqual]", SubscriptBox["j", "3"]]]]]]]


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





2003-08-21