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DedekindEta




Mathematica Notation

Traditional Notation









Elliptic Functions > DedekindEta[z] > Specific values > Values at fixed points





http://functions.wolfram.com/09.49.03.0001.01









  


  








Input Form





DedekindEta[I] == ((1/2) EllipticThetaPrime[1, 0, E^(-Pi)])^(1/3)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["DedekindEta", "[", "\[ImaginaryI]", "]"]], "\[Equal]", SuperscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "0", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "\[Pi]"]]]]], "]"]]]], ")"]], RowBox[List["1", "/", "3"]]]]]]]








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> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#8520; </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Eta]&quot;, &quot;(&quot;, TagBox[&quot;\[ImaginaryI]&quot;, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mo> &#10869; </mo> <mroot> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <msubsup> <mi> &#977; </mi> <mn> 1 </mn> <mo> &#8242; </mo> </msubsup> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> &#960; </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 3 </mn> </mroot> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> DedekindEta </ci> <imaginaryi /> </apply> <apply> <power /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <apply> <ci> Subscript </ci> <ci> &#977; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 0 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DedekindEta", "[", "\[ImaginaryI]", "]"]], "]"]], "\[RuleDelayed]", SuperscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "0", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "\[Pi]"]]]]], "]"]]]], ")"]], RowBox[List["1", "/", "3"]]]]]]]


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





2001-10-29