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http://functions.wolfram.com/06.16.21.0001.01
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Integrate[HarmonicNumber[z], z] == EulerGamma z + LogGamma[z + 1]
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["HarmonicNumber", "[", "z", "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["EulerGamma", " ", "z"]], "+", RowBox[List["LogGamma", "[", RowBox[List["z", "+", "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> <mrow> <mo> ∫ </mo> <mrow> <msub> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mi> z </mi> </msub> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[EulerGamma]] </annotation> </semantics> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mi> logΓ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <ci> HarmonicNumber </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <eulergamma /> <ci> z </ci> </apply> <apply> <ci> LogGamma </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["HarmonicNumber", "[", "z_", "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["EulerGamma", " ", "z"]], "+", RowBox[List["LogGamma", "[", RowBox[List["z", "+", "1"]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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