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http://functions.wolfram.com/06.16.04.0003.01
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Singularities[HarmonicNumber[z], z] ==
{SequenceList[{-k, 1}, Element[k, Integers] && k > 0],
{ComplexInfinity, Infinity}}
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Cell[BoxData[RowBox[List[RowBox[List["Singularities", "[", RowBox[List[RowBox[List["HarmonicNumber", "[", "z", "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List["SequenceList", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "k"]], ",", "1"]], "}"]], ",", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "\[And]", RowBox[List["k", ">", "0"]]]]]], "]"]], ",", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "\[Infinity]"]], "}"]]]], "}"]]]]]]
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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> <msub> <mi> 𝒮𝒾𝓃ℊ </mi> <mi> z </mi> </msub> <mo> ( </mo> <msub> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mi> z </mi> </msub> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mo> - </mo> <mi> k </mi> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> } </mo> </mrow> <mo> /; </mo> <mrow> <mi> k </mi> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <mover> <mi> ∞ </mi> <mo> ~ </mo> </mover> <mo> , </mo> <mi> ∞ </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> 𝒮𝒾𝓃ℊ </ci> <ci> z </ci> </apply> <apply> <ci> HarmonicNumber </ci> <ci> z </ci> </apply> </apply> <list> <list> <apply> <ci> Condition </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <cn type='integer'> 1 </cn> </list> <apply> <in /> <ci> k </ci> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> </apply> </list> <list> <apply> <ci> OverTilde </ci> <infinity /> </apply> <infinity /> </list> </list> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Singularities", "[", RowBox[List[RowBox[List["HarmonicNumber", "[", "z_", "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List[RowBox[List["SequenceList", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "k"]], ",", "1"]], "}"]], ",", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", ">", "0"]]]]]], "]"]], ",", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "\[Infinity]"]], "}"]]]], "}"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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