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variants of this functions
EllipticThetaPrime




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticThetaPrime[1,z,q] > General characteristics > Domain and analyticity





http://functions.wolfram.com/09.05.04.0001.01









  


  








Input Form





DomainAndRange[Function[{one, z, q}, EllipticThetaPrime[1, z, q]]] == ProductSet[{1}, Complexes, Complexes] \[LongRightArrow] Complexes








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["one", ",", "z", ",", "q"]], "}"]], ",", " ", RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]]]], "]"]], "]"]], " ", "\[Equal]", "\[IndentingNewLine]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List[RowBox[List["{", "1", "}"]], ",", "Complexes", ",", "Complexes"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]








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> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> * </mo> <mi> z </mi> <mo> * </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <mrow> <msubsup> <mi> &#977; </mi> <mn> 1 </mn> <mo> &#8242; </mo> </msubsup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8759; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <mn> 1 </mn> <mo> } </mo> </mrow> <mo> &#8855; </mo> <mi> &#8450; </mi> <mo> &#8855; </mo> <mi> &#8450; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <mi> &#8450; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <apply> <times /> <cn type='integer'> 1 </cn> <ci> z </ci> <ci> q </ci> </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> <ci> z </ci> <ci> q </ci> </apply> </apply> <apply> <ci> LongRightArrow </ci> <apply> <ci> CircleTimes </ci> <list> <cn type='integer'> 1 </cn> </list> <ci> &#8450; </ci> <ci> &#8450; </ci> </apply> <ci> &#8450; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["one_", ",", "z_", ",", "q_"]], "}"]], ",", RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "z_", ",", "q_"]], "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List[RowBox[List["{", "1", "}"]], ",", "Complexes", ",", "Complexes"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]


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





2001-10-29