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SixJSymbol






Mathematica Notation

Traditional Notation









Hypergeometric Functions > SixJSymbol[{j1,j2,j3},{j4,j5,j6}] > Generating functions





http://functions.wolfram.com/07.40.11.0001.01









  


  










Input Form





SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 4], Subscript[j, 5], Subscript[j, 6]}] == ((Sqrt[(1 + Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 3])!] Sqrt[(1 + Subscript[j, 3] + Subscript[j, 4] + Subscript[j, 5])!] Sqrt[(1 + Subscript[j, 2] + Subscript[j, 4] + Subscript[j, 6])!] Sqrt[(1 + Subscript[j, 1] + Subscript[j, 5] + Subscript[j, 6])!])/ (Sqrt[(Subscript[j, 1] + Subscript[j, 2] - Subscript[j, 3])!] Sqrt[(Subscript[j, 1] - Subscript[j, 2] + Subscript[j, 3])!] Sqrt[(-Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 3])!] Sqrt[(Subscript[j, 3] + Subscript[j, 4] - Subscript[j, 5])!] Sqrt[(Subscript[j, 3] - Subscript[j, 4] + Subscript[j, 5])!] Sqrt[(-Subscript[j, 3] + Subscript[j, 4] + Subscript[j, 5])!] Sqrt[(Subscript[j, 2] + Subscript[j, 4] - Subscript[j, 6])!] Sqrt[(Subscript[j, 1] + Subscript[j, 5] - Subscript[j, 6])!] Sqrt[(Subscript[j, 2] - Subscript[j, 4] + Subscript[j, 6])!] Sqrt[(-Subscript[j, 2] + Subscript[j, 4] + Subscript[j, 6])!] Sqrt[(Subscript[j, 1] - Subscript[j, 5] + Subscript[j, 6])!] Sqrt[(-Subscript[j, 1] + Subscript[j, 5] + Subscript[j, 6])!])) SeriesTerm[1/(1 + u v z + u w y + v w x + x y z + u v x y + u w x z + v w y z)^2, {u, 0, 2 Subscript[j, 1]}, {v, 0, 2 Subscript[j, 2]}, {w, 0, 2 Subscript[j, 3]}, {x, 0, 2 Subscript[j, 4]}, {y, 0, 2 Subscript[j, 5]}, {z, 0, 2 Subscript[j, 6]}] /; \[ScriptCapitalP]\[ScriptH]\[ScriptY]\[ScriptS]\[ScriptI]\[ScriptC]\ \[ScriptA]\[ScriptL]\[ScriptCapitalQ][{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[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"]]], "}"]]]], "]"]], " ", "\[Equal]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", SubscriptBox["j", "3"], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "5"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "6"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", SubscriptBox["j", "1"], "+", SubscriptBox["j", "5"], "+", SubscriptBox["j", "6"]]], ")"]], "!"]]]]], ")"]], "/", RowBox[List["(", RowBox[List[SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "-", SubscriptBox["j", "3"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SubscriptBox["j", "1"]]], "+", SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "3"], "+", SubscriptBox["j", "4"], "-", SubscriptBox["j", "5"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "3"], "-", SubscriptBox["j", "4"], "+", SubscriptBox["j", "5"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SubscriptBox["j", "3"]]], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "5"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "2"], "+", SubscriptBox["j", "4"], "-", SubscriptBox["j", "6"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "5"], "-", SubscriptBox["j", "6"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "2"], "-", SubscriptBox["j", "4"], "+", SubscriptBox["j", "6"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SubscriptBox["j", "2"]]], "+", SubscriptBox["j", "4"], "+", SubscriptBox["j", "6"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["j", "5"], "+", SubscriptBox["j", "6"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SubscriptBox["j", "1"]]], "+", SubscriptBox["j", "5"], "+", SubscriptBox["j", "6"]]], ")"]], "!"]]]]], ")"]]]], RowBox[List["SeriesTerm", "[", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["u", " ", "v", " ", "z"]], "+", RowBox[List["u", " ", "w", " ", "y"]], "+", RowBox[List["v", " ", "w", " ", "x"]], "+", RowBox[List["x", " ", "y", " ", "z"]], "+", RowBox[List["u", " ", "v", " ", "x", " ", "y"]], "+", RowBox[List["u", " ", "w", " ", "x", " ", "z"]], "+", RowBox[List["v", " ", "w", " ", "y", " ", "z"]]]], ")"]], "2"]], ",", RowBox[List["{", RowBox[List["u", ",", "0", ",", RowBox[List["2", SubscriptBox["j", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["v", ",", "0", ",", RowBox[List["2", SubscriptBox["j", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["w", ",", "0", ",", RowBox[List["2", SubscriptBox["j", "3"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["x", ",", "0", ",", RowBox[List["2", SubscriptBox["j", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["y", ",", "0", ",", RowBox[List["2", SubscriptBox["j", "5"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["z", ",", "0", ",", RowBox[List["2", SubscriptBox["j", "6"]]]]], "}"]]]], "]"]]]]]], "/;", RowBox[List["\[ScriptCapitalP]\[ScriptH]\[ScriptY]\[ScriptS]\[ScriptI]\[ScriptC]\[ScriptA]\[ScriptL]\[ScriptCapitalQ]", "[", 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> <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> <mo> &#10869; </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mrow> <mo> ( </mo> <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> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <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> 6 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mrow> <mo> ( </mo> <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> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! 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</mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <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> 6 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <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> 6 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> [ </mo> <mrow> <msup> <mi> u </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> </msup> <mtext> </mtext> <mo> , </mo> <msup> <mi> v </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> </msup> <mo> , </mo> <msup> <mi> w </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> </msup> <mo> , </mo> <msup> <mi> x </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mrow> </msup> <mo> , </mo> <msup> <mi> y </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> </msup> <mo> , </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> </msup> </mrow> <mo> ] </mo> </mrow> <mo> &#8290; </mo> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> v </mi> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> + </mo> <mrow> <mi> u </mi> <mo> &#8290; </mo> <mi> v </mi> <mo> &#8290; </mo> <mi> y </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> + </mo> <mrow> <mi> u </mi> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> + </mo> <mrow> <mi> y </mi> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> + </mo> <mrow> <mi> u </mi> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> <mo> + </mo> <mrow> <mi> u </mi> <mo> &#8290; </mo> <mi> v </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mi> v </mi> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mi> y </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> &#119979;&#119997;&#120014;&#120008;&#119998;&#119992;&#119990;&#8467;&#119980; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <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> 3 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <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> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <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> <mo> &#10869; </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mrow> <mo> ( </mo> <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> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <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> 6 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mrow> <mo> ( </mo> <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> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <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> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <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> 6 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <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> 6 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> <mo> + </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> [ </mo> <mrow> <msup> <mi> u </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 1 </mn> </msub> </mrow> </msup> <mtext> </mtext> <mo> , </mo> <msup> <mi> v </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 2 </mn> </msub> </mrow> </msup> <mo> , </mo> <msup> <mi> w </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 3 </mn> </msub> </mrow> </msup> <mo> , </mo> <msup> <mi> x </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 4 </mn> </msub> </mrow> </msup> <mo> , </mo> <msup> <mi> y </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 5 </mn> </msub> </mrow> </msup> <mo> , </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> j </mi> <mn> 6 </mn> </msub> </mrow> </msup> </mrow> <mo> ] </mo> </mrow> <mo> &#8290; </mo> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> v </mi> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> + </mo> <mrow> <mi> u </mi> <mo> &#8290; </mo> <mi> v </mi> <mo> &#8290; </mo> <mi> y </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> + </mo> <mrow> <mi> u </mi> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> + </mo> <mrow> <mi> y </mi> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> + </mo> <mrow> <mi> u </mi> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> <mo> + </mo> <mrow> <mi> u </mi> <mo> &#8290; </mo> <mi> v </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mi> v </mi> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mi> y </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> &#119979;&#119997;&#120014;&#120008;&#119998;&#119992;&#119990;&#8467;&#119980; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <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> 3 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <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> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





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