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http://functions.wolfram.com/10.02.06.0002.02
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ZetaClassical[s, a] \[Proportional] 1/(s - 1) - PolyGamma[a] (1 + O[s - 1])
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Cell[BoxData[RowBox[List[RowBox[List["ZetaClassical", "[", RowBox[List["s", ",", "a"]], "]"]], "\[Proportional]", RowBox[List[FractionBox["1", RowBox[List["s", "-", "1"]]], "-", RowBox[List[RowBox[List["PolyGamma", "[", "a", "]"]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["s", "-", "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> <semantics> <mrow> <mover> <mi> ζ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> s </mi> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[OverscriptBox["\[Zeta]", "^"], "(", RowBox[List[TagBox["s", Rule[Editable, True]], ",", TagBox["a", Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2], Zeta[$CellContext`e1, $CellContext`e2]]]] </annotation> </semantics> <mo> ∝ </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> s </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> - </mo> <mrow> <mrow> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> Zeta </ci> <ci> s </ci> <ci> a </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> s </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> PolyGamma </ci> <ci> a </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <apply> <plus /> <ci> s </ci> <cn type='integer'> -1 </cn> </apply> </apply> </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_", ",", "a_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", RowBox[List["s", "-", "1"]]], "-", RowBox[List[RowBox[List["PolyGamma", "[", "a", "]"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["s", "-", "1"]], "]"]]]], ")"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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