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; }

 SixJSymbol

 http://functions.wolfram.com/07.40.23.0022.01

 Input Form

 Sum[(2 k + 1) (2 l + 1) NineJSymbol[{Subscript[j, 1], Subscript[j, 2], k}, {Subscript[j, 3], Subscript[j, 4], l}, {Subscript[j, 5], Subscript[j, 6], Subscript[j, 7]}] SixJSymbol[{Subscript[j, 1], Subscript[j, 2], k}, {l, Subscript[j, 7], Subscript[j, 8]}] SixJSymbol[{Subscript[j, 3], Subscript[j, 4], l}, {Subscript[j, 2], Subscript[j, 8], Subscript[j, 9]}], {k, Abs[Subscript[j, 1] - Subscript[j, 2]], Subscript[j, 1] + Subscript[j, 2]}, {l, Max[Abs[Subscript[j, 3] - Subscript[j, 4]], Abs[Subscript[j, 7] - k]], Min[Subscript[j, 3] + Subscript[j, 4], Subscript[j, 7] + k]}] == ((-1)^(2 Subscript[j, 8])/ (2 Subscript[j, 6] + 1)) KroneckerDelta[Subscript[j, 6], Subscript[j, 9]] SixJSymbol[{Subscript[j, 5], Subscript[j, 9], Subscript[j, 7]}, {Subscript[j, 8], Subscript[j, 1], Subscript[j, 3]}] /; \[ScriptCapitalT]\[ScriptR]\[ScriptI]\[ScriptA]\[ScriptN]\[ScriptG]\ \[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\[ScriptCapitalQ][Subscript[j, 2], Subscript[j, 4], Subscript[j, 6]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["Abs", "[", RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "2"]]], "]"]]]], RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["l", "=", RowBox[List["Max", "[", RowBox[List[RowBox[List["Abs", "[", RowBox[List[SubscriptBox["j", "3"], "-", SubscriptBox["j", "4"]]], "]"]], ",", RowBox[List["Abs", "[", RowBox[List[SubscriptBox["j", "7"], "-", "k"]], "]"]]]], "]"]]]], RowBox[List["Min", "[", RowBox[List[RowBox[List[SubscriptBox["j", "3"], "+", SubscriptBox["j", "4"]]], ",", RowBox[List[SubscriptBox["j", "7"], "+", "k"]]]], "]"]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", "k"]], "+", "1"]], ")"]], RowBox[List["(", RowBox[List[RowBox[List["2", "l"]], "+", "1"]], ")"]], RowBox[List["NineJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "2"], ",", "k"]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["j", "4"], ",", "l"]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox["j", "6"], ",", SubscriptBox["j", "7"]]], "}"]]]], "]"]], RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "2"], ",", "k"]], "}"]], ",", RowBox[List["{", RowBox[List["l", ",", SubscriptBox["j", "7"], ",", SubscriptBox["j", "8"]]], "}"]]]], "]"]], RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["j", "4"], ",", "l"]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["j", "8"], ",", SubscriptBox["j", "9"]]], "}"]]]], "]"]]]]]]]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", SubscriptBox["j", "8"]]]], RowBox[List[RowBox[List["2", SubscriptBox["j", "6"]]], "+", "1"]]], RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox["j", "9"]]], "]"]], RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox["j", "9"], ",", SubscriptBox["j", "7"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "8"], ",", SubscriptBox["j", "1"], ",", SubscriptBox["j", "3"]]], "}"]]]], "]"]]]]]], "/;", RowBox[List["\[ScriptCapitalT]\[ScriptR]\[ScriptI]\[ScriptA]\[ScriptN]\[ScriptG]\[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\[ScriptCapitalQ]", "[", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["j", "4"], ",", SubscriptBox["j", "6"]]], "]"]]]]]]

 MathML Form

 k = "\[LeftBracketingBar]" j 1 - j 2 "\[RightBracketingBar]" j 1 + j 2 l = max ( "\[LeftBracketingBar]" j 3 - j 4 "\[RightBracketingBar]" , "\[LeftBracketingBar]" j 7 - k "\[RightBracketingBar]" ) min ( j 3 + j 4 , k + j 7 ) ( 2 k + 1 ) ( 2 l + 1 ) { j 1 j 2 k j 3 j 4 l j 5 j 6 j 7 } { TagBox[StyleBox["{", Rule[SpanMaxSize, DirectedInfinity[1]]], SixJSymbol] j 1 j 2 k l j 7 j 8 } TagBox[StyleBox["}", Rule[SpanMaxSize, DirectedInfinity[1]]], SixJSymbol] { TagBox[StyleBox["{", Rule[SpanMaxSize, DirectedInfinity[1]]], SixJSymbol] j 3 j 4 l j 2 j 8 j 9 } TagBox[StyleBox["}", Rule[SpanMaxSize, DirectedInfinity[1]]], SixJSymbol] ( - 1 ) 2 j 8 2 j 6 + 1 δ KroneckerDelta j 6 , j 9 { TagBox[StyleBox["{", Rule[SpanMaxSize, DirectedInfinity[1]]], SixJSymbol] j 5 j 9 j 7 j 8 j 1 j 3 } TagBox[StyleBox["}", Rule[SpanMaxSize, DirectedInfinity[1]]], SixJSymbol] /; 𝒯𝓇𝒾𝒶𝓃ℊ𝓊ℓ𝒶𝓇𝒬 ( j 2 , j 4 , j 6 ) Condition l Subscript j 3 -1 Subscript j 4 Subscript j 7 -1 k Subscript j 3 Subscript j 4 k Subscript j 7 k Subscript j 1 -1 Subscript j 2 Subscript j 1 Subscript j 2 2 k 1 2 l 1 Subscript j 1 Subscript j 2 k Subscript j 3 Subscript j 4 l Subscript j 5 Subscript j 6 Subscript j 7 SixJSymbol Subscript j 1 Subscript j 2 k l Subscript j 7 Subscript j 8 SixJSymbol Subscript j 3 Subscript j 4 l Subscript j 2 Subscript j 8 Subscript j 9 -1 2 Subscript j 8 2 Subscript j 6 1 -1 KroneckerDelta Subscript j 6 Subscript j 9 SixJSymbol Subscript j 5 Subscript j 9 Subscript j 7 Subscript j 8 Subscript j 1 Subscript j 3 𝒯𝓇𝒾𝒶𝓃ℊ𝓊ℓ𝒶𝓇𝒬 Subscript j 2 Subscript j 4 Subscript j 6 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["Abs", "[", RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "2"]]], "]"]]]], RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["l_", "=", RowBox[List["Max", "[", RowBox[List[RowBox[List["Abs", "[", RowBox[List[SubscriptBox["j", "3"], "-", SubscriptBox["j", "4"]]], "]"]], ",", RowBox[List["Abs", "[", RowBox[List[SubscriptBox["j", "7"], "-", "k"]], "]"]]]], "]"]]]], RowBox[List["Min", "[", RowBox[List[RowBox[List[SubscriptBox["j", "3"], "+", SubscriptBox["j", "4"]]], ",", RowBox[List[SubscriptBox["j", "7"], "+", "k"]]]], "]"]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "l_"]], "+", "1"]], ")"]], " ", RowBox[List["NineJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "2"], ",", "k"]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["j", "4"], ",", "l_"]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox["j", "6"], ",", SubscriptBox["j", "7"]]], "}"]]]], "]"]], " ", RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "2"], ",", "k"]], "}"]], ",", RowBox[List["{", RowBox[List["l_", ",", SubscriptBox["j", "7"], ",", SubscriptBox["j", "8"]]], "}"]]]], "]"]], " ", RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["j", "4"], ",", "l_"]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["j", "8"], ",", SubscriptBox["j", "9"]]], "}"]]]], "]"]]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", " ", SubscriptBox["j", "8"]]]], " ", RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox["j", "9"]]], "]"]], " ", RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox["j", "9"], ",", SubscriptBox["j", "7"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "8"], ",", SubscriptBox["j", "1"], ",", SubscriptBox["j", "3"]]], "}"]]]], "]"]]]], RowBox[List[RowBox[List["2", " ", SubscriptBox["j", "6"]]], "+", "1"]]], "/;", RowBox[List["\[ScriptCapitalT]\[ScriptR]\[ScriptI]\[ScriptA]\[ScriptN]\[ScriptG]\[ScriptU]\[ScriptL]\[ScriptA]\[ScriptR]\[ScriptCapitalQ]", "[", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["j", "4"], ",", SubscriptBox["j", "6"]]], "]"]]]]]]]]

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

 2001-12-21