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http://functions.wolfram.com/10.02.04.0028.01
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BranchCuts[ZetaClassicalRegularized[s, a], a] ==
{{Interval[{-Infinity, 0}], -I}}
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Cell[BoxData[RowBox[List[RowBox[List["BranchCuts", "[", RowBox[List[RowBox[List["ZetaClassicalRegularized", "[", RowBox[List["s", ",", "a"]], "]"]], ",", "a"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List["{", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", RowBox[List["-", "\[ImaginaryI]"]]]], "}"]], "}"]]]]]]
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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> a </mi> </msub> <mo> ( </mo> <semantics> <mrow> <mover> <mi> ζ </mi> <mo> ~ </mo> </mover> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[OverscriptBox["\[Zeta]", "~"], RowBox[List["(", RowBox[List[TagBox["s", Rule[Editable, True]], ",", "a"]], ")"]]]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2, $CellContext`e3], LerchPhi[$CellContext`e1, $CellContext`e2, $CellContext`e3]]]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2], Zeta[$CellContext`e1, $CellContext`e2]]]] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> </mrow> <mo> } </mo> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msub> <mi> ℬ𝒞 </mi> <mi> a </mi> </msub> <mo> ( </mo> <semantics> <mrow> <mover> <mi> ζ </mi> <mo> ~ </mo> </mover> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[OverscriptBox["\[Zeta]", "~"], RowBox[List["(", RowBox[List[TagBox["s", Rule[Editable, True]], ",", "a"]], ")"]]]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2, $CellContext`e3], LerchPhi[$CellContext`e1, $CellContext`e2, $CellContext`e3]]]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2], Zeta[$CellContext`e1, $CellContext`e2]]]] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> </mrow> <mo> } </mo> </mrow> <mo> } </mo> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BranchCuts", "[", RowBox[List[RowBox[List["ZetaClassicalRegularized", "[", RowBox[List["s_", ",", "a_"]], "]"]], ",", "a_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List["{", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", RowBox[List["-", "\[ImaginaryI]"]]]], "}"]], "}"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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