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http://functions.wolfram.com/09.49.16.0003.01
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DedekindEta[-(1/z)] == (Sqrt[z] DedekindEta[z])/E^((Pi I)/4)
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Cell[BoxData[RowBox[List[RowBox[List["DedekindEta", "[", RowBox[List["-", FractionBox["1", "z"]]], "]"]], "\[Equal]", RowBox[List[SqrtBox["z"], SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"]]]], RowBox[List["DedekindEta", "[", "z", "]"]]]]]]]]
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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> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Eta]", "(", TagBox[RowBox[List["-", FractionBox["1", "z"]]], Rule[Editable, True]], ")"]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> <mn> 4 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mi> η </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Eta]", "(", TagBox["z", Rule[Editable, True]], ")"]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> DedekindEta </ci> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DedekindEta", "[", RowBox[List["-", FractionBox["1", "z_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox["z"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]]], " ", RowBox[List["DedekindEta", "[", "z", "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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