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http://functions.wolfram.com/10.02.16.0010.01
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ZetaClassical[s, 2 a] == (ZetaClassical[s, a] + ZetaClassical[s, 1/2 + a])/2^s
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Cell[BoxData[RowBox[List[RowBox[List["ZetaClassical", "[", RowBox[List["s", ",", RowBox[List["2", " ", "a"]]]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List["-", "s"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["ZetaClassical", "[", RowBox[List["s", ",", "a"]], "]"]], "+", RowBox[List["ZetaClassical", "[", RowBox[List["s", ",", RowBox[List[FractionBox["1", "2"], "+", "a"]]]], "]"]]]], ")"]]]]]]]]
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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> <mover> <mi> ζ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> s </mi> <mo> , </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[OverscriptBox["\[Zeta]", "^"], "(", RowBox[List[TagBox["s", Rule[Editable, True]], ",", TagBox[RowBox[List["2", " ", "a"]], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2], Zeta[$CellContext`e1, $CellContext`e2]]]] </annotation> </semantics> <mo>  </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mover> <mi> ζ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> s </mi> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mover> <mi> ζ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> s </mi> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Zeta </ci> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <apply> <plus /> <apply> <apply> <ci> OverHat </ci> <ci> ζ </ci> </apply> <ci> s </ci> <ci> a </ci> </apply> <apply> <apply> <ci> OverHat </ci> <ci> ζ </ci> </apply> <ci> s </ci> <apply> <plus /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ZetaClassical", "[", RowBox[List["s_", ",", RowBox[List["2", " ", "a_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", RowBox[List["-", "s"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["ZetaClassical", "[", RowBox[List["s", ",", "a"]], "]"]], "+", RowBox[List["ZetaClassical", "[", RowBox[List["s", ",", RowBox[List[FractionBox["1", "2"], "+", "a"]]]], "]"]]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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