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http://functions.wolfram.com/10.03.04.0009.01
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BranchCuts[RiemannSiegelTheta[z], z] ==
{{Interval[{(-I) Infinity, -(I/2)}], 1}, {Interval[{I/2, I Infinity}], -1}}
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Cell[BoxData[RowBox[List[RowBox[List["BranchCuts", "[", RowBox[List[RowBox[List["RiemannSiegelTheta", "[", "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["-", FractionBox["\[ImaginaryI]", "2"]]]]], "}"]], "]"]], ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[FractionBox["\[ImaginaryI]", "2"], ",", RowBox[List["\[ImaginaryI]", " ", "\[Infinity]"]]]], "}"]], "]"]], ",", RowBox[List["-", "1"]]]], "}"]]]], "}"]]]]]]
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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> <msub> <mi> ℬ𝒞 </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <semantics> <mi> ϑ </mi> <annotation encoding='Mathematica'> TagBox["\[CurlyTheta]", RiemannSiegelTheta] </annotation> </semantics> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mi> ∞ </mi> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mi> ⅈ </mi> <mn> 2 </mn> </mfrac> </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> <mfrac> <mi> ⅈ </mi> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> ∞ </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> ℬ𝒞 </ci> <ci> z </ci> </apply> <apply> <ci> RiemannSiegelTheta </ci> <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'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </list> <cn type='integer'> 1 </cn> </list> <list> <list> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <infinity /> </apply> </list> <cn type='integer'> -1 </cn> </list> </list> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BranchCuts", "[", RowBox[List[RowBox[List["RiemannSiegelTheta", "[", "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["-", FractionBox["\[ImaginaryI]", "2"]]]]], "}"]], "]"]], ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[FractionBox["\[ImaginaryI]", "2"], ",", RowBox[List["\[ImaginaryI]", " ", "\[Infinity]"]]]], "}"]], "]"]], ",", RowBox[List["-", "1"]]]], "}"]]]], "}"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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