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SixJSymbol






Mathematica Notation

Traditional Notation









Hypergeometric Functions > SixJSymbol[{j1,j2,j3},{j4,j5,j6}] > Primary definition





http://functions.wolfram.com/07.40.02.0004.01









  


  










Input Form





\[ScriptCapitalP]\[ScriptH]\[ScriptY]\[ScriptS]\[ScriptI]\[ScriptC]\[ScriptA]\ \[ScriptL]\[ScriptCapitalQ][{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 4], Subscript[j, 5], Subscript[j, 6]}] == \[ScriptCapitalT]\[ScriptR]\[ScriptI]\[ScriptA]\[ScriptN]\[ScriptG]\ \[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\[ScriptCapitalQ][Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]] && \[ScriptCapitalT]\[ScriptR]\[ScriptI]\ \[ScriptA]\[ScriptN]\[ScriptG]\[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\ \[ScriptCapitalQ][Subscript[j, 1], Subscript[j, 5], Subscript[j, 6]] && \[ScriptCapitalT]\[ScriptR]\[ScriptI]\[ScriptA]\[ScriptN]\[ScriptG]\ \[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\[ScriptCapitalQ][Subscript[j, 2], Subscript[j, 4], Subscript[j, 6]] && \[ScriptCapitalT]\[ScriptR]\[ScriptI]\ \[ScriptA]\[ScriptN]\[ScriptG]\[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\ \[ScriptCapitalQ][Subscript[j, 3], Subscript[j, 4], Subscript[j, 5]]










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["j", "2"], ",", SubscriptBox["j", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox["j", "5"], ",", SubscriptBox["j", "6"]]], "}"]]]], "]"]], "\[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["\[ScriptCapitalT]\[ScriptR]\[ScriptI]\[ScriptA]\[ScriptN]\[ScriptG]\[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\[ScriptCapitalQ]", "[", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "5"], ",", SubscriptBox["j", "6"]]], "]"]], "\[And]", RowBox[List["\[ScriptCapitalT]\[ScriptR]\[ScriptI]\[ScriptA]\[ScriptN]\[ScriptG]\[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\[ScriptCapitalQ]", "[", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["j", "4"], ",", SubscriptBox["j", "6"]]], "]"]], "\[And]", RowBox[List["\[ScriptCapitalT]\[ScriptR]\[ScriptI]\[ScriptA]\[ScriptN]\[ScriptG]\[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\[ScriptCapitalQ]", "[", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["j", "4"], ",", SubscriptBox["j", "5"]]], "]"]]]]]]










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["j", "2"], ",", SubscriptBox["j", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox["j", "5"], ",", SubscriptBox["j", "6"]]], "}"]]]], "]"]], "\[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["\[ScriptCapitalT]\[ScriptR]\[ScriptI]\[ScriptA]\[ScriptN]\[ScriptG]\[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\[ScriptCapitalQ]", "[", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "5"], ",", SubscriptBox["j", "6"]]], "]"]], "&&", RowBox[List["\[ScriptCapitalT]\[ScriptR]\[ScriptI]\[ScriptA]\[ScriptN]\[ScriptG]\[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\[ScriptCapitalQ]", "[", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["j", "4"], ",", SubscriptBox["j", "6"]]], "]"]], "&&", RowBox[List["\[ScriptCapitalT]\[ScriptR]\[ScriptI]\[ScriptA]\[ScriptN]\[ScriptG]\[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\[ScriptCapitalQ]", "[", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["j", "4"], ",", SubscriptBox["j", "5"]]], "]"]]]]]]










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





2007-05-02





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