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variants of this functions
EllipticTheta




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[4,z,q] > General characteristics > Natural boundary of analyticity





http://functions.wolfram.com/09.04.04.0016.01









  


  








Input Form





AnalyticityBoundary[EllipticTheta[4, q, z], z] == {Exp[I Interval[{-Pi, Pi}]]}








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["AnalyticityBoundary", "[", RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "q", ",", "z"]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List["Exp", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Pi]"]], ",", " ", "\[Pi]"]], "}"]], "]"]]]], "]"]], "}"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> &#119964;&#8492; </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <msup> <mi> &#8519; </mi> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#960; </mi> </mrow> <mo> , </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msub> <mi> &#119964;&#8492; </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <msup> <mi> &#8519; </mi> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#960; </mi> </mrow> <mo> , </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> } </mo> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AnalyticityBoundary", "[", RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "q_", ",", "z_"]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Pi]"]], ",", "\[Pi]"]], "}"]], "]"]]]]], "}"]]]]]]


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





2001-10-29