Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











SixJSymbol




Mathematica Notation

Traditional Notation









Hypergeometric Functions > SixJSymbol[{j1,j2,j3},{j4,j5,j6}] > Operations > Limit operation





http://functions.wolfram.com/07.40.25.0001.01









  


  








Input Form





Limit[(-1)^(2 (n - Subscript[j, 1] - Subscript[j, 4])) Sqrt[2 Subscript[j, 6] + 2 n + 1] SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {n + Subscript[j, 4], n + Subscript[j, 5], n + Subscript[j, 6]}], n -> Infinity] == ThreeJSymbol[{Subscript[j, 1], Subscript[j, 6] - Subscript[j, 5]}, {Subscript[j, 2], Subscript[j, 4] - Subscript[j, 6]}, {Subscript[j, 3], Subscript[j, 5] - Subscript[j, 4]}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["n", "-", SubscriptBox["j", "1"], "-", SubscriptBox["j", "4"]]], ")"]]]]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", SubscriptBox["j", "6"]]], "+", RowBox[List["2", " ", "n"]], "+", "1"]]], RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "2"], ",", SubscriptBox["j", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["n", "+", SubscriptBox["j", "4"]]], ",", RowBox[List["n", "+", SubscriptBox["j", "5"]]], ",", RowBox[List["n", "+", SubscriptBox["j", "6"]]]]], "}"]]]], "]"]]]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]], "\[Equal]", RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", RowBox[List[SubscriptBox["j", "6"], "-", SubscriptBox["j", "5"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", RowBox[List[SubscriptBox["j", "4"], "-", SubscriptBox["j", "6"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", RowBox[List[SubscriptBox["j", "5"], "-", SubscriptBox["j", "4"]]]]], "}"]]]], "]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <munder> <mi> lim </mi> <mrow> <mi> n </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mi> &#8734; </mi> </mrow> </munder> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <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> <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> <mrow> <mi> n </mi> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mrow> </mtd> <mtd> <mrow> <mi> n </mi> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> </mtd> <mtd> <mrow> <mi> n </mi> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </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> <mo> &#10869; </mo> <mrow> <semantics> <mo> ( </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;(&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </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> <mrow> <msub> <mi> j </mi> <mn> 6 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mrow> </mtd> </mtr> </mtable> <mtext> &#8287; </mtext> <semantics> <mo> ) </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;)&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <limit /> <bvar> <ci> n </ci> </bvar> <condition> <apply> <tendsto /> <ci> n </ci> <infinity /> </apply> </condition> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <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> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <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> <plus /> <ci> n </ci> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <plus /> <ci> n </ci> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <plus /> <ci> n </ci> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </apply> </list> </apply> </apply> </apply> <apply> <ci> ThreeJSymbol </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> </list> <list> <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'> 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> </list> <list> <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'> 5 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </list> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["n_", "-", SubscriptBox["j", "1"], "-", SubscriptBox["j", "4"]]], ")"]]]]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", SubscriptBox["j", "6"]]], "+", RowBox[List["2", " ", "n_"]], "+", "1"]]], " ", RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "2"], ",", SubscriptBox["j", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["n_", "+", SubscriptBox["j", "4"]]], ",", RowBox[List["n_", "+", SubscriptBox["j", "5"]]], ",", RowBox[List["n_", "+", SubscriptBox["j", "6"]]]]], "}"]]]], "]"]]]], ",", RowBox[List["n_", "\[Rule]", "\[Infinity]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", RowBox[List[SubscriptBox["j", "6"], "-", SubscriptBox["j", "5"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", RowBox[List[SubscriptBox["j", "4"], "-", SubscriptBox["j", "6"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", RowBox[List[SubscriptBox["j", "5"], "-", SubscriptBox["j", "4"]]]]], "}"]]]], "]"]]]]]]


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





2001-10-29