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DedekindEta




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.49.27.0006.01









  


  








Input Form





DedekindEta[z]^24 == D[KleinInvariantJ[z], z]^6/ ((48 Pi^2)^3 KleinInvariantJ[z]^4 (1 - KleinInvariantJ[z])^3) /; Im[z] > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", "z", "]"]], "24"], "\[Equal]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["KleinInvariantJ", "[", "z", "]"]]]], ")"]], "6"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["48", " ", SuperscriptBox["\[Pi]", "2"]]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["KleinInvariantJ", "[", "z", "]"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["KleinInvariantJ", "[", "z", "]"]]]], ")"]], "3"]]]]]], "/;", " ", RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "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> <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> 24 </mn> </msup> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 48 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <semantics> <mrow> <mi> J </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;J&quot;, &quot;(&quot;, TagBox[&quot;z&quot;, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[KleinInvariantJ[Slot[1]]]]] </annotation> </semantics> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mrow> <mi> J </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;J&quot;, &quot;(&quot;, TagBox[&quot;z&quot;, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[KleinInvariantJ[Slot[1]]]]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mo> &#8706; </mo> <semantics> <mrow> <mi> J </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;J&quot;, &quot;(&quot;, TagBox[&quot;z&quot;, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[KleinInvariantJ[Slot[1]]]]] </annotation> </semantics> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <apply> <ci> DedekindEta </ci> <ci> z </ci> </apply> <cn type='integer'> 24 </cn> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> 48 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> KleinInvariantJ </ci> <ci> z </ci> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> KleinInvariantJ </ci> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> KleinInvariantJ </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <gt /> <apply> <imaginary /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["DedekindEta", "[", "z_", "]"]], "24"], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z"]]], RowBox[List["KleinInvariantJ", "[", "z", "]"]]]], ")"]], "6"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["48", " ", SuperscriptBox["\[Pi]", "2"]]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["KleinInvariantJ", "[", "z", "]"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["KleinInvariantJ", "[", "z", "]"]]]], ")"]], "3"]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "0"]]]]]]]]


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





2001-10-29