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variants of this functions
HarmonicNumber




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > HarmonicNumber[z,r] > General characteristics > Poles and essential singularities > With respect to r





http://functions.wolfram.com/06.17.04.0003.01









  


  








Input Form





Singularities[HarmonicNumber[z, r], r] == {{ComplexInfinity, Infinity}}








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Singularities", "[", RowBox[List[RowBox[List["HarmonicNumber", "[", RowBox[List["z", ",", "r"]], "]"]], ",", "r"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "\[Infinity]"]], "}"]], "}"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> &#119982;&#119998;&#120003;&#8458; </mi> <mi> r </mi> </msub> <mo> ( </mo> <semantics> <mstyle scriptlevel='0'> <msubsup> <mi> H </mi> <mi> z </mi> <mrow> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </msubsup> </mstyle> <annotation encoding='Mathematica'> TagBox[StyleBox[SubsuperscriptBox[InterpretationBox[&quot;H&quot;, HarmonicNumber, Rule[Editable, False], Rule[Selectable, False]], &quot;z&quot;, RowBox[List[&quot;(&quot;, &quot;r&quot;, &quot;)&quot;]]], Rule[ScriptLevel, 0]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2], Zeta[$CellContext`e1, $CellContext`e2]]]] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mo> { </mo> <mrow> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> } </mo> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msub> <mi> &#119982;&#119998;&#120003;&#8458; </mi> <mi> r </mi> </msub> <mo> ( </mo> <semantics> <mstyle scriptlevel='0'> <msubsup> <mi> H </mi> <mi> z </mi> <mrow> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </msubsup> </mstyle> <annotation encoding='Mathematica'> TagBox[StyleBox[SubsuperscriptBox[InterpretationBox[&quot;H&quot;, HarmonicNumber, Rule[Editable, False], Rule[Selectable, False]], &quot;z&quot;, RowBox[List[&quot;(&quot;, &quot;r&quot;, &quot;)&quot;]]], Rule[ScriptLevel, 0]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2], Zeta[$CellContext`e1, $CellContext`e2]]]] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mo> { </mo> <mrow> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> } </mo> </mrow> <mo> } </mo> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Singularities", "[", RowBox[List[RowBox[List["HarmonicNumber", "[", RowBox[List["z_", ",", "r_"]], "]"]], ",", "r_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "\[Infinity]"]], "}"]], "}"]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29