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http://functions.wolfram.com/06.16.06.0024.01
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HarmonicNumber[z] \[Proportional] (Pi^2 z)/6 - Zeta[3] z^2 + (Pi^4 z^3)/90 +
O[z^4]
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Cell[BoxData[RowBox[List[RowBox[List["HarmonicNumber", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", "z"]], "6"], "-", RowBox[List[RowBox[List["Zeta", "[", "3", "]"]], SuperscriptBox["z", "2"]]], " ", "+", FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["z", "3"]]], "90"], "+", RowBox[List["O", "[", SuperscriptBox["z", "4"], "]"]]]]]]]]
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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> <msub> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mi> z </mi> </msub> <mo> ∝ </mo> <mrow> <mfrac> <mrow> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mn> 6 </mn> </mfrac> <mo> - </mo> <mrow> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Rule[Editable, True]], ")"]], InterpretTemplate[Function[$CellContext`e, Zeta[$CellContext`e]]]] </annotation> </semantics> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mfrac> <mrow> <msup> <mi> π </mi> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mn> 90 </mn> </mfrac> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> HarmonicNumber </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> <apply> <power /> <cn type='integer'> 6 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 90 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HarmonicNumber", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", "z"]], "6"], "-", RowBox[List[RowBox[List["Zeta", "[", "3", "]"]], " ", SuperscriptBox["z", "2"]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["z", "3"]]], "90"], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "4"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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