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
 











ThreeJSymbol




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.39.23.0014.01









  


  








Input Form





Sum[(-1)^(Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 4] + Subscript[j, 5] + Subscript[j, 6] - Subscript[m, 1] - Subscript[m, 2] - Subscript[m, 4] - Subscript[m, 5] - Subscript[m, 6]) ThreeJSymbol[{Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 3], -Subscript[m, 3]}, {Subscript[j, 1], Subscript[m, 1]}] ThreeJSymbol[{Subscript[j, 1], -Subscript[m, 1]}, {Subscript[j, 5], Subscript[m, 5]}, {Subscript[j, 6], Subscript[m, 6]}] ThreeJSymbol[{Subscript[j, 5], -Subscript[m, 5]}, {Derivative[1][Subscript[j, 3]], Derivative[1][Subscript[m, 3]]}, {Subscript[j, 4], Subscript[m, 4]}] ThreeJSymbol[{Subscript[j, 4], -Subscript[m, 4]}, {Subscript[j, 2], -Subscript[m, 2]}, {Subscript[j, 6], -Subscript[m, 6]}], {Subscript[m, 1], -Subscript[j, 1], Subscript[j, 1]}, {Subscript[m, 2], -Subscript[j, 2], Subscript[j, 2]}, {Subscript[m, 4], -Subscript[j, 4], Subscript[j, 4]}, {Subscript[m, 5], -Subscript[j, 5], Subscript[j, 5]}, {Subscript[m, 6], -Subscript[j, 6], Subscript[j, 6]}] == ((-1)^(Subscript[j, 3] - Subscript[m, 3])/(2 Subscript[j, 3] + 1)) KroneckerDelta[Subscript[j, 3], Derivative[1][Subscript[j, 3]]] KroneckerDelta[Subscript[m, 3], Derivative[1][Subscript[m, 3]]] SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 4], Subscript[j, 5], Subscript[j, 6]}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "1"], "=", RowBox[List["-", SubscriptBox["j", "1"]]]]], SubscriptBox["j", "1"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "2"], "=", RowBox[List["-", SubscriptBox["j", "2"]]]]], SubscriptBox["j", "2"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "4"], "=", RowBox[List["-", SubscriptBox["j", "4"]]]]], SubscriptBox["j", "4"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "5"], "=", RowBox[List["-", SubscriptBox["j", "5"]]]]], SubscriptBox["j", "5"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m", "6"], "=", RowBox[List["-", SubscriptBox["j", "6"]]]]], SubscriptBox["j", "6"]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "5"], "+", SubscriptBox["j", "6"], "-", SubscriptBox["m", "1"], "-", SubscriptBox["m", "2"], "-", SubscriptBox["m", "4"], "-", SubscriptBox["m", "5"], "-", SubscriptBox["m", "6"]]]], RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", RowBox[List["-", SubscriptBox["m", "3"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m", "1"]]], "}"]]]], "]"]], RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", RowBox[List["-", SubscriptBox["m", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox["m", "5"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox["m", "6"]]], "}"]]]], "]"]], RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", RowBox[List["-", SubscriptBox["m", "5"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubsuperscriptBox["j", "3", "\[Prime]"], ",", SubsuperscriptBox["m", "3", "\[Prime]"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox["m", "4"]]], "}"]]]], "]"]], RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", RowBox[List["-", SubscriptBox["m", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", RowBox[List["-", SubscriptBox["m", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", RowBox[List["-", SubscriptBox["m", "6"]]]]], "}"]]]], "]"]]]]]]]]]]]]]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[SubscriptBox["j", "3"], "-", SubscriptBox["m", "3"]]]], RowBox[List[RowBox[List["2", SubscriptBox["j", "3"]]], "+", "1"]]], RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["j", "3"], ",", SubsuperscriptBox["j", "3", "\[Prime]"]]], "]"]], RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["m", "3"], ",", SubsuperscriptBox["m", "3", "\[Prime]"]]], "]"]], RowBox[List["SixJSymbol", "[", 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"]]], "}"]]]], "]"]]]]]]]]








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> 1 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> </mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> </mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> m </mi> <mn> 4 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mrow> </mrow> <msub> <mi> j </mi> <mn> 4 </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> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> m </mi> <mn> 6 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> </mrow> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </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> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 4 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 5 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 6 </mn> </msub> </mrow> </msup> <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> 2 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <mrow> <mo> - </mo> <msub> <mi> m </mi> <mn> 3 </mn> </msub> </mrow> </mtd> <mtd> <msub> <mi> m </mi> <mn> 1 </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> 1 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo> - </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mrow> </mtd> <mtd> <msub> <mi> m </mi> <mn> 5 </mn> </msub> </mtd> <mtd> <msub> <mi> m </mi> <mn> 6 </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> 5 </mn> </msub> </mtd> <mtd> <msubsup> <mi> j </mi> <mn> 3 </mn> <mo> &#8242; </mo> </msubsup> </mtd> <mtd> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo> - </mo> <msub> <mi> m </mi> <mn> 5 </mn> </msub> </mrow> </mtd> <mtd> <msubsup> <mi> m </mi> <mn> 3 </mn> <mo> &#8242; </mo> </msubsup> </mtd> <mtd> <msub> <mi> m </mi> <mn> 4 </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> 4 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo> - </mo> <msub> <mi> m </mi> <mn> 4 </mn> </msub> </mrow> </mtd> <mtd> <mrow> <mo> - </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> </mtd> <mtd> <mrow> <mo> - </mo> <msub> <mi> m </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]]], ThreeJSymbol] </annotation> </semantics> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 3 </mn> </msub> </mrow> </msup> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <msub> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> , </mo> <msubsup> <mi> j </mi> <mn> 3 </mn> <mo> &#8242; </mo> </msubsup> </mrow> </msub> <mo> &#8290; </mo> <msub> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <msub> <mi> m </mi> <mn> 3 </mn> </msub> <mo> , </mo> <msubsup> <mi> m </mi> <mn> 3 </mn> <mo> &#8242; </mo> </msubsup> </mrow> </msub> <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> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mtd> <mtd> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </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> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 6 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </apply> </lowlimit> <uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </uplimit> <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'> 4 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> </apply> </lowlimit> <uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> </lowlimit> <uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> </lowlimit> <uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <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'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> <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> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> </apply> <apply> <ci> ThreeJSymbol </ci> <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> <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'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </list> </apply> <apply> <ci> ThreeJSymbol </ci> <list> <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> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> </list> <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> </apply> <apply> <ci> ThreeJSymbol </ci> <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> <list> <apply> <partialdiff /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <partialdiff /> <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> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> </list> </apply> <apply> <ci> ThreeJSymbol </ci> <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'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </list> <list> <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> m </ci> <cn type='integer'> 6 </cn> </apply> </apply> </list> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <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> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> KroneckerDelta </ci> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> <apply> <partialdiff /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <ci> KroneckerDelta </ci> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> <apply> <partialdiff /> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> </apply> </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> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </list> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m_", "1"], "=", RowBox[List["-", SubscriptBox["j", "1"]]]]], SubscriptBox["j", "1"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m_", "2"], "=", RowBox[List["-", SubscriptBox["j", "2"]]]]], SubscriptBox["j", "2"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m_", "4"], "=", RowBox[List["-", SubscriptBox["j", "4"]]]]], SubscriptBox["j", "4"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m_", "5"], "=", RowBox[List["-", SubscriptBox["j", "5"]]]]], SubscriptBox["j", "5"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m_", "6"], "=", RowBox[List["-", SubscriptBox["j", "6"]]]]], SubscriptBox["j", "6"]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "5"], "+", SubscriptBox["j", "6"], "-", SubscriptBox["m_", "1"], "-", SubscriptBox["m_", "2"], "-", SubscriptBox["m_", "4"], "-", SubscriptBox["m_", "5"], "-", SubscriptBox["m_", "6"]]]], " ", RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", RowBox[List["-", SubscriptBox["m_", "3"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m_", "1"]]], "}"]]]], "]"]], " ", RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", RowBox[List["-", SubscriptBox["m_", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox["m_", "5"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox["m_", "6"]]], "}"]]]], "]"]], " ", RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", RowBox[List["-", SubscriptBox["m_", "5"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SuperscriptBox[SubscriptBox["j", "3"], "\[Prime]", Rule[MultilineFunction, None]], ",", SuperscriptBox[SubscriptBox["m_", "3"], "\[Prime]", Rule[MultilineFunction, None]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox["m_", "4"]]], "}"]]]], "]"]], " ", RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", RowBox[List["-", SubscriptBox["m_", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", RowBox[List["-", SubscriptBox["m_", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", RowBox[List["-", SubscriptBox["m_", "6"]]]]], "}"]]]], "]"]]]]]]]]]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[SubscriptBox["j", "3"], "-", SubscriptBox["mm", "3"]]]], " ", RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["j", "3"], ",", SuperscriptBox[SubscriptBox["j", "3"], "\[Prime]", Rule[MultilineFunction, None]]]], "]"]], " ", RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["mm", "3"], ",", SuperscriptBox[SubscriptBox["mm", "3"], "\[Prime]", Rule[MultilineFunction, None]]]], "]"]], " ", RowBox[List["SixJSymbol", "[", 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"]]], "}"]]]], "]"]]]], RowBox[List[RowBox[List["2", " ", SubscriptBox["j", "3"]]], "+", "1"]]]]]]]


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





2001-12-21