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http://functions.wolfram.com/09.05.04.0003.01
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EllipticThetaPrime[1, z, -q] == Exp[(-((I Pi)/4)) Sign[Im[q]]]
EllipticThetaPrime[1, z, q]
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Cell[BoxData[RowBox[List[RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "z", ",", RowBox[List["-", "q"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Exp", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "4"]]], " ", RowBox[List["Sign", "[", RowBox[List["Im", "[", "q", "]"]], "]"]]]], "]"]], " ", RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]]]]]]]]
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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> <mrow> <msubsup> <mi> ϑ </mi> <mn> 1 </mn> <mo> ′ </mo> </msubsup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mrow> <mo> - </mo> <mi> q </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ι </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mn> 4 </mn> </mfrac> </mrow> <mo> ⁢ </mo> <mrow> <mi> sgn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msubsup> <mi> ϑ </mi> <mn> 1 </mn> <mo> ′ </mo> </msubsup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </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> ϑ </ci> <cn type='integer'> 1 </cn> </apply> </apply> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> </apply> <apply> <times /> <apply> <exp /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> ι </ci> <pi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Sign </ci> <apply> <imaginary /> <ci> q </ci> </apply> </apply> </apply> </apply> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <apply> <ci> Subscript </ci> <ci> ϑ </ci> <cn type='integer'> 1 </cn> </apply> </apply> <ci> z </ci> <ci> q </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "z_", ",", RowBox[List["-", "q_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["-", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], ")"]]]], ")"]], " ", RowBox[List["Sign", "[", RowBox[List["Im", "[", "q", "]"]], "]"]]]]], " ", RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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