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http://functions.wolfram.com/10.01.17.0006.01
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Zeta[s] == Gamma[1 - s] 2^s Pi^(s - 1) Sin[(Pi s)/2] Zeta[1 - s]
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Cell[BoxData[RowBox[List[RowBox[List["Zeta", "[", "s", "]"]], "\[Equal]", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "-", "s"]], "]"]], SuperscriptBox["2", "s"], " ", SuperscriptBox["\[Pi]", RowBox[List["s", "-", "1"]]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", "s"]], "2"], "]"]], RowBox[List["Zeta", "[", RowBox[List["1", "-", "s"]], "]"]]]]]]]]
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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> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["s", Rule[Editable, True]], ")"]], InterpretTemplate[Function[$CellContext`e, Zeta[$CellContext`e]]]] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mn> 2 </mn> <mi> s </mi> </msup> <mo> ⁢ </mo> <msup> <mi> π </mi> <mrow> <mi> s </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mtext> </mtext> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox[RowBox[List["1", "-", "s"]], Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Zeta </ci> <ci> s </ci> </apply> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> <apply> <power /> <pi /> <apply> <plus /> <ci> s </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <ci> s </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Zeta </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Zeta", "[", "s_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "-", "s"]], "]"]], " ", SuperscriptBox["2", "s"], " ", SuperscriptBox["\[Pi]", RowBox[List["s", "-", "1"]]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", "s"]], "2"], "]"]], " ", RowBox[List["Zeta", "[", RowBox[List["1", "-", "s"]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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