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variants of this functions
EllipticThetaPrime




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticThetaPrime[3,z,q] > Specific values > Specialized values > For fixed q





http://functions.wolfram.com/09.07.03.0006.01









  


  








Input Form





EllipticThetaPrime[3, Pi/4 + (Pi/2) m, q] == 4 (-1)^(m - 1) DedekindEta[-((4 I Log[q])/Pi)]^3 /; Element[m, Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EllipticThetaPrime", "[", RowBox[List["3", ",", RowBox[List[FractionBox["\[Pi]", "4"], "+", RowBox[List[FractionBox["\[Pi]", "2"], " ", "m"]]]], ",", "q"]], "]"]], "\[Equal]", RowBox[List["4", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["m", "-", "1"]]], SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["-", FractionBox[RowBox[List["4", "\[ImaginaryI]", " ", RowBox[List["Log", "[", "q", "]"]]]], "\[Pi]"]]], "]"]], "3"]]]]], "/;", RowBox[List["m", "\[Element]", "Integers"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msubsup> <mi> &#977; </mi> <mn> 3 </mn> <mo> &#8242; </mo> </msubsup> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mi> &#960; </mi> <mn> 4 </mn> </mfrac> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> </mrow> <mi> &#960; </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Eta]&quot;, &quot;(&quot;, TagBox[RowBox[List[&quot;-&quot;, FractionBox[RowBox[List[&quot;4&quot;, &quot; &quot;, &quot;\[ImaginaryI]&quot;, &quot; &quot;, RowBox[List[&quot;log&quot;, &quot;(&quot;, &quot;q&quot;, &quot;)&quot;]]]], &quot;\[Pi]&quot;]]], Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> <mn> 3 </mn> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> m </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <apply> <ci> Subscript </ci> <ci> &#977; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <pi /> <ci> m </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> q </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <ci> DedekindEta </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <imaginaryi /> <apply> <ln /> <ci> q </ci> </apply> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <in /> <ci> m </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticThetaPrime", "[", RowBox[List["3", ",", RowBox[List[FractionBox["\[Pi]", "4"], "+", FractionBox[RowBox[List["\[Pi]", " ", "m_"]], "2"]]], ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["m", "-", "1"]]], " ", SuperscriptBox[RowBox[List["DedekindEta", "[", RowBox[List["-", FractionBox[RowBox[List["4", " ", "\[ImaginaryI]", " ", RowBox[List["Log", "[", "q", "]"]]]], "\[Pi]"]]], "]"]], "3"]]], "/;", RowBox[List["m", "\[Element]", "Integers"]]]]]]]]


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





2007-05-02