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DedekindEta






Mathematica Notation

Traditional Notation









Elliptic Functions > DedekindEta[z] > Identities > Functional identities





http://functions.wolfram.com/09.49.17.0008.01









  


  










Input Form





DedekindEta[z]^2 DedekindEta[4 z] DedekindEta[6 z]^9 + DedekindEta[2 z]^3 DedekindEta[3 z]^6 DedekindEta[12 z]^3 - 2 DedekindEta[z] DedekindEta[2 z] DedekindEta[3 z]^3 DedekindEta[4 z]^3 DedekindEta[6 z]^2 DedekindEta[12 z]^2 == 0










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", "z", "]"]], "2"], " ", RowBox[List["DedekindEta", "[", RowBox[List["4", " ", "z"]], "]"]], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["6", " ", "z"]], "]"]], "9"]]], "+", RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["2", " ", "z"]], "]"]], "3"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["3", " ", "z"]], "]"]], "6"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["12", " ", "z"]], "]"]], "3"]]], "-", RowBox[List["2", " ", RowBox[List["DedekindEta", "[", "z", "]"]], " ", RowBox[List["DedekindEta", "[", RowBox[List["2", " ", "z"]], "]"]], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["3", " ", "z"]], "]"]], "3"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["4", " ", "z"]], "]"]], "3"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["6", " ", "z"]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["12", " ", "z"]], "]"]], "2"]]]]], "\[Equal]", "0"]]]]










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> <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;, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 4 </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;4&quot;, &quot; &quot;, &quot;z&quot;]], Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mo> &#8290; </mo> <msup> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 6 </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;6&quot;, &quot; &quot;, &quot;z&quot;]], Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <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;, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </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;2&quot;, &quot; &quot;, &quot;z&quot;]], Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <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;]], Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 4 </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;4&quot;, &quot; &quot;, &quot;z&quot;]], Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 12 </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;12&quot;, &quot; &quot;, &quot;z&quot;]], Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 6 </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;6&quot;, &quot; &quot;, &quot;z&quot;]], Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <msup> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </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;2&quot;, &quot; &quot;, &quot;z&quot;]], Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 3 </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;]], Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 6 </mn> </msup> <mo> &#8290; </mo> <msup> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 12 </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;12&quot;, &quot; &quot;, &quot;z&quot;]], Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 3 </mn> </msup> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <ci> DedekindEta </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 6 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> DedekindEta </ci> <ci> z </ci> </apply> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 12 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 6 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 12 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", "z_", "]"]], "2"], " ", RowBox[List["DedekindEta", "[", RowBox[List["4", " ", "z_"]], "]"]], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["6", " ", "z_"]], "]"]], "9"]]], "+", RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["2", " ", "z_"]], "]"]], "3"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["3", " ", "z_"]], "]"]], "6"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["12", " ", "z_"]], "]"]], "3"]]], "-", RowBox[List["2", " ", RowBox[List["DedekindEta", "[", "z_", "]"]], " ", RowBox[List["DedekindEta", "[", RowBox[List["2", " ", "z_"]], "]"]], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["3", " ", "z_"]], "]"]], "3"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["4", " ", "z_"]], "]"]], "3"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["6", " ", "z_"]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["12", " ", "z_"]], "]"]], "2"]]]]], "]"]], "\[RuleDelayed]", "0"]]]]










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





2001-10-29





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