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DedekindEta






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.49.17.0007.01









  


  










Input Form





DedekindEta[6 z]^7/DedekindEta[3 z] == (DedekindEta[4 z]^3 DedekindEta[18 z]^9)/(DedekindEta[9 z]^3 DedekindEta[36 z]^3) - (DedekindEta[36 z]^3 DedekindEta[2 z]^9)/ (DedekindEta[z]^3 DedekindEta[4 z]^3)










Standard Form





Cell[BoxData[RowBox[List[FractionBox[SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["6", " ", "z"]], "]"]], "7"], RowBox[List["DedekindEta", "[", RowBox[List["3", " ", "z"]], "]"]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["4", " ", "z"]], "]"]], "3"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["18", " ", "z"]], "]"]], "9"]]], RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["9", " ", "z"]], "]"]], "3"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["36", " ", "z"]], "]"]], "3"]]]], "-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["36", " ", "z"]], "]"]], "3"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["2", " ", "z"]], "]"]], "9"]]], RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", "z", "]"]], "3"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["4", " ", "z"]], "]"]], "3"]]]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <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> 7 </mn> </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> </mfrac> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <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> 18 </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;18&quot;, &quot; &quot;, &quot;z&quot;]], Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 9 </mn> </msup> </mrow> <mrow> <msup> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 9 </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;9&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> 36 </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;36&quot;, &quot; &quot;, &quot;z&quot;]], Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <msup> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 36 </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;36&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> 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> 9 </mn> </msup> </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> 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> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 6 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 7 </cn> </apply> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <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'> 18 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 9 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 9 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 36 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 36 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 9 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <ci> DedekindEta </ci> <ci> z </ci> </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> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["6", " ", "z_"]], "]"]], "7"], RowBox[List["DedekindEta", "[", RowBox[List["3", " ", "z_"]], "]"]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["4", " ", "z"]], "]"]], "3"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["18", " ", "z"]], "]"]], "9"]]], RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["9", " ", "z"]], "]"]], "3"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["36", " ", "z"]], "]"]], "3"]]]], "-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["36", " ", "z"]], "]"]], "3"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["2", " ", "z"]], "]"]], "9"]]], RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", "z", "]"]], "3"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["4", " ", "z"]], "]"]], "3"]]]]]]]]]]










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





2001-10-29





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