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variants of this functions
EllipticThetaPrime




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticThetaPrime[1,z,q] > Specific values > Specialized values > For fixed q





http://functions.wolfram.com/09.05.03.0006.01









  


  








Input Form





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








Standard Form





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








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <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> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mi> &#964; </mi> </mfrac> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <msqrt> <mi> &#8520; </mi> </msqrt> </mrow> <mo> &#8290; </mo> <msup> <mi> &#964; </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <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> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#964; </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <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> <apply> <times /> <imaginaryi /> <pi /> <apply> <power /> <ci> &#964; </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <imaginaryi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> &#964; </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <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 /> <imaginaryi /> <pi /> <ci> &#964; </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "0", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "\[Tau]_"]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", SqrtBox["\[ImaginaryI]"]]], " ", SuperscriptBox["\[Tau]", RowBox[List["3", "/", "2"]]], " ", RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "0", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Tau]"]]]]], "]"]]]]]]]]


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





2001-10-29