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ThreeJSymbol




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ThreeJSymbol[{j1,m1},{j2,m2},{j3,m3}] > Summation > Finite summation > Involving three 3j symbols





http://functions.wolfram.com/07.39.23.0013.01









  


  








Input Form





Sum[ThreeJSymbol[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 3], Subscript[m, 3]}] ThreeJSymbol[{Subscript[j, 3], -Subscript[m, 3]}, {Subscript[j, 4], -Subscript[m, 4]}, {Subscript[j, 5], -Subscript[m, 5]}] ThreeJSymbol[{Subscript[j, 5], Subscript[m, 5]}, {Subscript[j, 6], Subscript[m, 6]}, {Subscript[j, 7], Subscript[m, 7]}], {Subscript[m, 3], -Subscript[j, 3], Subscript[j, 3]}, {Subscript[m, 5], -Subscript[j, 5], Subscript[j, 5]}] == Sum[(2 k + 1) (2 l + 1) ThreeJSymbol[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 6], Subscript[m, 6]}, {k, \[Kappa]}] ThreeJSymbol[{k, -\[Kappa]}, {Subscript[j, 4], -Subscript[m, 4]}, {l, -\[Lambda]}] ThreeJSymbol[{l, \[Lambda]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 7], Subscript[m, 7]}] NineJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 6], Subscript[j, 7], Subscript[j, 5]}, {k, l, Subscript[j, 4]}], {k, Abs[Subscript[j, 1] - Subscript[j, 6]], Subscript[j, 1] + Subscript[j, 6]}, {l, Max[Abs[Subscript[j, 4] - k], Abs[Subscript[j, 2] - Subscript[j, 7]]], Min[Subscript[j, 4] + k, Subscript[j, 2] + Subscript[j, 7]]}, {\[Kappa], -k, k}, {\[Lambda], -l, l}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "3"], "=", RowBox[List["-", SubscriptBox["j", "3"]]]]], SubscriptBox["j", "3"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "5"], "=", RowBox[List["-", SubscriptBox["j", "5"]]]]], SubscriptBox["j", "5"]], 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"]]], "}"]]]], "]"]], RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", RowBox[List["-", SubscriptBox["m", "3"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", RowBox[List["-", SubscriptBox["m", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", RowBox[List["-", SubscriptBox["m", "5"]]]]], "}"]]]], "]"]], RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox["m", "5"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox["m", "6"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "7"], ",", SubscriptBox["m", "7"]]], "}"]]]], "]"]]]]]]]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["Abs", "[", RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "6"]]], "]"]]]], RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "6"]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["l", "=", RowBox[List["Max", "[", RowBox[List[RowBox[List["Abs", "[", RowBox[List[SubscriptBox["j", "4"], "-", "k"]], "]"]], ",", RowBox[List["Abs", "[", RowBox[List[SubscriptBox["j", "2"], "-", SubscriptBox["j", "7"]]], "]"]]]], "]"]]]], RowBox[List["Min", "[", RowBox[List[RowBox[List[SubscriptBox["j", "4"], "+", "k"]], ",", RowBox[List[SubscriptBox["j", "2"], "+", SubscriptBox["j", "7"]]]]], "]"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["\[Kappa]", "=", RowBox[List["-", "k"]]]], "k"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["\[Lambda]", "=", RowBox[List["-", "l"]]]], "l"], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", "k"]], "+", "1"]], ")"]], RowBox[List["(", RowBox[List[RowBox[List["2", "l"]], "+", "1"]], ")"]], RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox["m", "6"]]], "}"]], ",", RowBox[List["{", RowBox[List["k", ",", "\[Kappa]"]], "}"]]]], "]"]], RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List["k", ",", RowBox[List["-", "\[Kappa]"]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", RowBox[List["-", SubscriptBox["m", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["l", ",", RowBox[List["-", "\[Lambda]"]]]], "}"]]]], "]"]], RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List["l", ",", "\[Lambda]"]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "7"], ",", SubscriptBox["m", "7"]]], "}"]]]], "]"]], RowBox[List["NineJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "2"], ",", SubscriptBox["j", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox["j", "7"], ",", SubscriptBox["j", "5"]]], "}"]], ",", RowBox[List["{", RowBox[List["k", ",", "l", ",", 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> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> m </mi> <mn> 3 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> m </mi> <mn> 5 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> </mrow> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </munderover> <mrow> <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> <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> &#8287; </mtext> <semantics> <mo> ) </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;)&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> </mrow> <mo> &#8290; </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> 3 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo> - </mo> <msub> <mi> m </mi> <mn> 3 </mn> </msub> </mrow> </mtd> <mtd> <mrow> <mo> - </mo> <msub> <mi> m </mi> <mn> 4 </mn> </msub> </mrow> </mtd> <mtd> <mrow> <mo> - </mo> <msub> <mi> m </mi> <mn> 5 </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> <mo> &#8290; </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> 5 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 7 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi> m </mi> <mn> 5 </mn> </msub> </mtd> <mtd> <msub> <mi> m </mi> <mn> 6 </mn> </msub> </mtd> <mtd> <msub> <mi> m </mi> <mn> 7 </mn> </msub> </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> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <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> 6 </mn> </msub> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> </mrow> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> l </mi> <mo> = </mo> <mrow> <mi> max </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> - </mo> <mi> k </mi> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> , </mo> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 7 </mn> </msub> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> min </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <mi> k </mi> </mrow> <mo> , </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 7 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> &#954; </mi> <mo> = </mo> <mrow> <mo> - </mo> <mi> k </mi> </mrow> </mrow> <mi> k </mi> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> &#955; </mi> <mo> = </mo> <mrow> <mo> - </mo> <mi> l </mi> </mrow> </mrow> <mi> l </mi> </munderover> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> l </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </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> 6 </mn> </msub> </mtd> <mtd> <mi> k </mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mtd> <mtd> <msub> <mi> m </mi> <mn> 6 </mn> </msub> </mtd> <mtd> <mi> &#954; </mi> </mtd> </mtr> </mtable> <mtext> &#8287; </mtext> <semantics> <mo> ) </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;)&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> </mrow> <mo> &#8290; </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> <mi> k </mi> </mtd> <mtd> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mtd> <mtd> <mi> l </mi> </mtd> </mtr> <mtr> <mtd> <mrow> <mo> - </mo> <mi> &#954; </mi> </mrow> </mtd> <mtd> <mrow> <mo> - </mo> <msub> <mi> m </mi> <mn> 4 </mn> </msub> </mrow> </mtd> <mtd> <mrow> <mo> - </mo> <mi> &#955; </mi> </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> <mo> &#8290; </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> <mi> l </mi> </mtd> <mtd> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 7 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi> &#955; </mi> </mtd> <mtd> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <msub> <mi> m </mi> <mn> 7 </mn> </msub> </mtd> </mtr> </mtable> <mtext> &#8287; </mtext> <semantics> <mo> ) </mo> <annotation encoding='Mathematica'> TagBox[StyleBox[&quot;)&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] </annotation> </semantics> </mrow> <mo> &#8290; </mo> <mrow> <mo> { </mo> <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> j </mi> <mn> 6 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 7 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi> k </mi> </mtd> <mtd> <mi> l </mi> </mtd> <mtd> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mtd> </mtr> </mtable> <mo> } </mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 5 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> </apply> </lowlimit> <uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </apply> </lowlimit> <uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </uplimit> <apply> <times /> <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> <ci> ThreeJSymbol </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> </apply> </list> <list> <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> m </ci> <cn type='integer'> 4 </cn> </apply> </apply> </list> <list> <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> m </ci> <cn type='integer'> 5 </cn> </apply> </apply> </list> </apply> <apply> <ci> ThreeJSymbol </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 5 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 6 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 7 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 7 </cn> </apply> </list> </apply> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> &#955; </ci> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <ci> l </ci> </apply> </lowlimit> <uplimit> <ci> l </ci> </uplimit> <apply> <sum /> <bvar> <ci> &#954; </ci> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </lowlimit> <uplimit> <ci> k </ci> </uplimit> <apply> <sum /> <bvar> <ci> l </ci> </bvar> <lowlimit> <apply> <max /> <apply> <abs /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> <apply> <abs /> <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'> 7 </cn> </apply> </apply> </apply> </apply> </apply> </lowlimit> <uplimit> <apply> <min /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <ci> k </ci> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> </uplimit> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <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'> 6 </cn> </apply> </apply> </apply> </apply> </lowlimit> <uplimit> <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'> 6 </cn> </apply> </apply> </uplimit> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> l </ci> </apply> <cn type='integer'> 1 </cn> </apply> <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'> 6 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 6 </cn> </apply> </list> <list> <ci> k </ci> <ci> &#954; </ci> </list> </apply> <apply> <ci> ThreeJSymbol </ci> <list> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#954; </ci> </apply> </list> <list> <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> m </ci> <cn type='integer'> 4 </cn> </apply> </apply> </list> <list> <ci> l </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#955; </ci> </apply> </list> </apply> <apply> <ci> ThreeJSymbol </ci> <list> <ci> l </ci> <ci> &#955; </ci> </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'> 7 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 7 </cn> </apply> </list> </apply> <list> <list> <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> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 7 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> </list> <list> <ci> k </ci> <ci> l </ci> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> </list> </list> </list> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-12-21