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KleinInvariantJ




Mathematica Notation

Traditional Notation









Elliptic Functions > KleinInvariantJ[z] > Representations through equivalent functions > With related functions > Involving other related functions





http://functions.wolfram.com/09.50.27.0010.01









  


  








Input Form





KleinInvariantJ[3 z] == ((DedekindEta[z]^12 + 3 DedekindEta[3 z]^12)^3 (DedekindEta[z]^12 + 27 DedekindEta[3 z]^12))/ (1728 DedekindEta[z]^12 DedekindEta[3 z]^36)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["KleinInvariantJ", "[", RowBox[List["3", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", "z", "]"]], "12"], "+", RowBox[List["3", " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["3", " ", "z"]], "]"]], "12"]]]]], ")"]], "3"], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", "z", "]"]], "12"], "+", RowBox[List["27", " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["3", " ", "z"]], "]"]], "12"]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["1728", " ", SuperscriptBox[RowBox[List["DedekindEta", "[", "z", "]"]], "12"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["3", " ", "z"]], "]"]], "36"]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mi> J </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;J&quot;, &quot;(&quot;, TagBox[RowBox[List[&quot;3&quot;, &quot; &quot;, &quot;z&quot;]], Identity, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[KleinInvariantJ[Slot[1]]]]] </annotation> </semantics> <mo> &#10869; </mo> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Eta]&quot;, &quot;(&quot;, TagBox[&quot;z&quot;, Identity, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 12 </mn> </msup> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msup> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Eta]&quot;, &quot;(&quot;, TagBox[RowBox[List[&quot;3&quot;, &quot; &quot;, &quot;z&quot;]], Identity, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 12 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Eta]&quot;, &quot;(&quot;, TagBox[&quot;z&quot;, Identity, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 12 </mn> </msup> <mo> + </mo> <mrow> <mn> 27 </mn> <mo> &#8290; </mo> <msup> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Eta]&quot;, &quot;(&quot;, TagBox[RowBox[List[&quot;3&quot;, &quot; &quot;, &quot;z&quot;]], Identity, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 12 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 1728 </mn> <mo> &#8290; </mo> <msup> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Eta]&quot;, &quot;(&quot;, TagBox[&quot;z&quot;, Identity, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 12 </mn> </msup> <mo> &#8290; </mo> <msup> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Eta]&quot;, &quot;(&quot;, TagBox[RowBox[List[&quot;3&quot;, &quot; &quot;, &quot;z&quot;]], Identity, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 36 </mn> </msup> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> KleinInvariantJ </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <ci> DedekindEta </ci> <ci> z </ci> </apply> <cn type='integer'> 12 </cn> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 12 </cn> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <power /> <apply> <ci> DedekindEta </ci> <ci> z </ci> </apply> <cn type='integer'> 12 </cn> </apply> <apply> <times /> <cn type='integer'> 27 </cn> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 12 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1728 </cn> <apply> <power /> <apply> <ci> DedekindEta </ci> <ci> z </ci> </apply> <cn type='integer'> 12 </cn> </apply> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 36 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KleinInvariantJ", "[", RowBox[List["3", " ", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", "z", "]"]], "12"], "+", RowBox[List["3", " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["3", " ", "z"]], "]"]], "12"]]]]], ")"]], "3"], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", "z", "]"]], "12"], "+", RowBox[List["27", " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["3", " ", "z"]], "]"]], "12"]]]]], ")"]]]], RowBox[List["1728", " ", SuperscriptBox[RowBox[List["DedekindEta", "[", "z", "]"]], "12"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["3", " ", "z"]], "]"]], "36"]]]]]]]]


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





2007-05-02