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http://functions.wolfram.com/09.49.03.0001.01
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DedekindEta[I] == ((1/2) EllipticThetaPrime[1, 0, E^(-Pi)])^(1/3)
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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"]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mi> η </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> ⅈ </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Eta]", "(", TagBox["\[ImaginaryI]", Rule[Editable, True]], ")"]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mo> ⩵ </mo> <mroot> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <msubsup> <mi> ϑ </mi> <mn> 1 </mn> <mo> ′ </mo> </msubsup> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <mi> π </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> ϑ </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>
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| 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"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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