|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/09.03.03.0004.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
EllipticTheta[3, 0, E^(Pi I \[Tau])] == DedekindEta[\[Tau]]^5/
(DedekindEta[2 \[Tau]]^2 DedekindEta[\[Tau]/2]^2) /; Im[\[Tau]] > 0
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "0", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "\[Tau]"]]]]], "]"]], "\[Equal]", FractionBox[SuperscriptBox[RowBox[List["DedekindEta", "[", "\[Tau]", "]"]], "5"], RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["2", " ", "\[Tau]"]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", FractionBox["\[Tau]", "2"], "]"]], "2"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "\[Tau]", "]"]], ">", "0"]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <mi> ϑ </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> τ </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <msup> <semantics> <mrow> <mi> η </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Eta]", "(", TagBox["\[Tau]", Rule[Editable, True]], ")"]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 5 </mn> </msup> <mrow> <msup> <semantics> <mrow> <mi> η </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> τ </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Eta]", "(", TagBox[RowBox[List["2", " ", "\[Tau]"]], Rule[Editable, True]], ")"]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <semantics> <mrow> <mi> η </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> τ </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Eta]", "(", TagBox[FractionBox["\[Tau]", "2"], Rule[Editable, True]], ")"]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> <mo> > </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 3 </cn> <cn type='integer'> 0 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <pi /> <imaginaryi /> <ci> τ </ci> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <ci> DedekindEta </ci> <ci> τ </ci> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> τ </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <ci> τ </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <gt /> <apply> <imaginary /> <ci> τ </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "0", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "\[Tau]_"]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["DedekindEta", "[", "\[Tau]", "]"]], "5"], RowBox[List[SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["2", " ", "\[Tau]"]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", FractionBox["\[Tau]", "2"], "]"]], "2"]]]], "/;", RowBox[List[RowBox[List["Im", "[", "\[Tau]", "]"]], ">", "0"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
){kind=small}
