Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

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}] > General characteristics > Domain and analyticity





http://functions.wolfram.com/07.39.04.0001.01









  


  










Input Form





DomainAndRange[Function[{{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 3], Subscript[m, 3]}}, ThreeJSymbol[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 3], Subscript[m, 3]}]]] == PowerSet[SetUnion[Rationals, Rationals], 3] \[LongRightArrow] Complexes










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", 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"]]], "}"]]]], "}"]], ",", " ", "\[IndentingNewLine]", 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"]]], "}"]]]], "]"]]]], " ", "]"]], " ", "]"]], "\[Equal]", "\[IndentingNewLine]", RowBox[List[RowBox[List["PowerSet", "[", RowBox[List[RowBox[List["SetUnion", "[", RowBox[List["Rationals", ",", " ", "Rationals"]], "]"]], ",", "3"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]










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> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> * </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> &#8902; </mo> <mrow> <mrow> <mo> { </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> * </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> * </mo> <mrow> <mo> { </mo> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> * </mo> <msub> <mi> m </mi> <mn> 3 </mn> </msub> </mrow> <mo> } </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <semantics> <mrow> <mo> ( </mo> <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> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[TagBox[StyleBox[&quot;(&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol], &quot;\[MediumSpace]&quot;, GridBox[List[List[SubscriptBox[&quot;j&quot;, &quot;1&quot;], SubscriptBox[&quot;j&quot;, &quot;2&quot;], SubscriptBox[&quot;j&quot;, &quot;3&quot;]], List[SubscriptBox[&quot;m&quot;, &quot;1&quot;], SubscriptBox[&quot;m&quot;, &quot;2&quot;], SubscriptBox[&quot;m&quot;, &quot;3&quot;]]]], &quot;\[MediumSpace]&quot;, TagBox[StyleBox[&quot;)&quot;, Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol]]], ClebschGordan, Rule[StripWrapperBoxes, True]] </annotation> </semantics> </mrow> <mo> &#8759; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mi> &#8474; </mi> <mo> &#8855; </mo> <mi> &#8474; </mi> </mrow> <mo> } </mo> </mrow> <mo> &#8855; </mo> <mrow> <mo> { </mo> <mrow> <mi> &#8474; </mi> <mo> &#8855; </mo> <mi> &#8474; </mi> </mrow> <mo> } </mo> </mrow> <mo> &#8855; </mo> <mrow> <mo> { </mo> <mrow> <mi> &#8474; </mi> <mo> &#8855; </mo> <mi> &#8474; </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <mi> &#8450; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <apply> <ci> Star </ci> <list> <apply> <times /> <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> </apply> </list> <apply> <times /> <list> <apply> <times /> <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> </apply> </list> <list> <apply> <times /> <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> </apply> </list> </apply> </apply> <apply> <ci> ClebschGordan </ci> <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> </apply> <apply> <ci> LongRightArrow </ci> <apply> <ci> CircleTimes </ci> <list> <apply> <ci> CircleTimes </ci> <ci> &#8474; </ci> <ci> &#8474; </ci> </apply> </list> <list> <apply> <ci> CircleTimes </ci> <ci> &#8474; </ci> <ci> &#8474; </ci> </apply> </list> <list> <apply> <ci> CircleTimes </ci> <ci> &#8474; </ci> <ci> &#8474; </ci> </apply> </list> </apply> <ci> &#8450; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", 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", "1"], ",", SubscriptBox["m_", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["m_", "3"]]], "}"]]]], "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["PowerSet", "[", RowBox[List[RowBox[List["SetUnion", "[", RowBox[List["Rationals", ",", "Rationals"]], "]"]], ",", "3"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]










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





2001-10-29





© 1998- Wolfram Research, Inc.