html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 ThreeJSymbol

 http://functions.wolfram.com/07.39.07.0009.01

 Input Form

 Abs[ThreeJSymbol[{Subscript[j, 1], 0}, {Subscript[j, 2], 0}, {Subscript[j, 3], 0}]]^2 == (1/2) Integrate[Sin[\[CurlyTheta]] LegendreP[Subscript[j, 1], Cos[\[CurlyTheta]]] LegendreP[Subscript[j, 2], Cos[\[CurlyTheta]]] LegendreP[Subscript[j, 3], Cos[\[CurlyTheta]]], {\[CurlyTheta], 0, Pi}] /; Element[Subscript[j, 1], Integers] && Subscript[j, 1] >= 0 && Element[Subscript[j, 2], Integers] && Subscript[j, 2] >= 0 && Element[Subscript[j, 3], Integers] && Subscript[j, 3] >= 0 && Abs[Subscript[j, 1] - Subscript[j, 2]] <= Subscript[j, 3] <= Subscript[j, 1] + Subscript[j, 2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Abs", "[", RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", "0"]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", "0"]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", "0"]], "}"]]]], "]"]], "]"]], "2"], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Pi]"], RowBox[List[RowBox[List["Sin", "[", "\[CurlyTheta]", "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List[SubscriptBox["j", "1"], ",", RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]]]], "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List[SubscriptBox["j", "2"], ",", RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]]]], "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List[SubscriptBox["j", "3"], ",", RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]]]], "]"]], " ", RowBox[List["\[DifferentialD]", "\[CurlyTheta]"]]]]]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["j", "1"], "\[Element]", "Integers"]], "\[And]", RowBox[List[SubscriptBox["j", "1"], "\[GreaterEqual]", "0"]], "\[And]", RowBox[List[SubscriptBox["j", "2"], "\[Element]", "Integers"]], "\[And]", RowBox[List[SubscriptBox["j", "2"], "\[GreaterEqual]", "0"]], "\[And]", RowBox[List[SubscriptBox["j", "3"], "\[Element]", "Integers"]], "\[And]", RowBox[List[SubscriptBox["j", "3"], "\[GreaterEqual]", "0"]], "\[And]", RowBox[List[RowBox[List["Abs", "[", RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "2"]]], "]"]], "\[LessEqual]", SubscriptBox["j", "3"], "\[LessEqual]", RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"]]]]]]]]]]]

 MathML Form

 "\[LeftBracketingBar]" ( TagBox[StyleBox["(", Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] j 1 j 2 j 3 0 0 0 ) TagBox[StyleBox[")", Rule[SpanMaxSize, DirectedInfinity[1]]], ThreeJSymbol] "\[RightBracketingBar]" 2 1 2 0 π sin ( ϑ ) P TagBox["P", LegendreP] j 1 ( cos ( ϑ ) ) P TagBox["P", LegendreP] j 2 ( cos ( ϑ ) ) P TagBox["P", LegendreP] j 3 ( cos ( ϑ ) ) ϑ /; j 1 j 2 j 3 "\[LeftBracketingBar]" j 1 - j 2 "\[RightBracketingBar]" j 3 j 1 + j 2 Condition ThreeJSymbol Subscript j 1 0 Subscript j 2 0 Subscript j 3 0 2 1 2 ϑ 0 ϑ LegendreP Subscript j 1 ϑ LegendreP Subscript j 2 ϑ LegendreP Subscript j 3 ϑ Subscript j 1 Subscript j 2 Subscript j 3 Subscript j 1 -1 Subscript j 2 Subscript j 3 Subscript j 1 Subscript j 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["Abs", "[", RowBox[List["ThreeJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", "0"]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", "0"]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", "0"]], "}"]]]], "]"]], "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Pi]"], RowBox[List[RowBox[List[RowBox[List["Sin", "[", "\[CurlyTheta]", "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List[SubscriptBox["j", "1"], ",", RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]]]], "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List[SubscriptBox["j", "2"], ",", RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]]]], "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List[SubscriptBox["j", "3"], ",", RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]]]], "]"]]]], RowBox[List["\[DifferentialD]", "\[CurlyTheta]"]]]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["j", "1"], "\[Element]", "Integers"]], "&&", RowBox[List[SubscriptBox["j", "1"], "\[GreaterEqual]", "0"]], "&&", RowBox[List[SubscriptBox["j", "2"], "\[Element]", "Integers"]], "&&", RowBox[List[SubscriptBox["j", "2"], "\[GreaterEqual]", "0"]], "&&", RowBox[List[SubscriptBox["j", "3"], "\[Element]", "Integers"]], "&&", RowBox[List[SubscriptBox["j", "3"], "\[GreaterEqual]", "0"]], "&&", RowBox[List[RowBox[List["Abs", "[", RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "2"]]], "]"]], "\[LessEqual]", SubscriptBox["j", "3"], "\[LessEqual]", RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"]]]]]]]]]]]]]

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

 2001-12-21

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