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RamanujanTauTheta




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RamanujanTauTheta[z] > General characteristics > Branch cuts





http://functions.wolfram.com/10.12.04.0009.01









  


  








Input Form





BranchCuts[RamanujanTauTheta[z], z] == {{Interval[{(-I) Infinity, -6 I}], 1}, {Interval[{6 I, I Infinity}], -1}}








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["BranchCuts", "[", RowBox[List[RowBox[List["RamanujanTauTheta", "[", "z", "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "\[Infinity]"]], ",", RowBox[List[RowBox[List["-", "6"]], "\[ImaginaryI]"]]]], "}"]], "]"]], ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["6", "\[ImaginaryI]"]], ",", RowBox[List["\[ImaginaryI]", " ", "\[Infinity]"]]]], "}"]], "]"]], ",", RowBox[List["-", "1"]]]], "}"]]]], "}"]]]]]]








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> &#8492;&#119966; </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <semantics> <mi> &#964;&#952; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Tau]\[Theta]&quot;, RiemannSiegelTheta] </annotation> </semantics> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mtext> </mtext> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mo> , </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#8734; </mi> </mrow> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#8492;&#119966; </ci> <ci> z </ci> </apply> <apply> <apply> <ci> RiemannSiegelTheta </ci> <ci> &#964;&#952; </ci> </apply> <ci> z </ci> </apply> </apply> <list> <list> <list> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <infinity /> </apply> <apply> <times /> <cn type='integer'> -6 </cn> <imaginaryi /> </apply> </list> <cn type='integer'> 1 </cn> </list> <list> <list> <apply> <times /> <cn type='integer'> 6 </cn> <imaginaryi /> </apply> <apply> <times /> <imaginaryi /> <infinity /> </apply> </list> <cn type='integer'> -1 </cn> </list> </list> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BranchCuts", "[", RowBox[List[RowBox[List["RamanujanTauTheta", "[", "z_", "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "\[Infinity]"]], ",", RowBox[List[RowBox[List["-", "6"]], " ", "\[ImaginaryI]"]]]], "}"]], "]"]], ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["6", " ", "\[ImaginaryI]"]], ",", RowBox[List["\[ImaginaryI]", " ", "\[Infinity]"]]]], "}"]], "]"]], ",", RowBox[List["-", "1"]]]], "}"]]]], "}"]]]]]]


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





2007-05-02