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variants of this functions
HarmonicNumber




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > HarmonicNumber[z] > General characteristics > Poles and essential singularities





http://functions.wolfram.com/06.16.04.0004.01









  


  








Input Form





Residue[HarmonicNumber[z], {z, -k}] == -1 /; Element[k, Integers] && k > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Residue", "[", RowBox[List[RowBox[List["HarmonicNumber", "[", "z", "]"]], ",", RowBox[List["{", RowBox[List["z", ",", " ", RowBox[List["-", "k"]]]], "}"]]]], "]"]], " ", "\[Equal]", RowBox[List["-", "1"]]]], " ", "/;", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "\[And]", RowBox[List["k", ">", "0"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <msub> <mi> res </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> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> k </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <apply> <apply> <ci> Subscript </ci> <ci> res </ci> <ci> z </ci> </apply> <apply> <ci> HarmonicNumber </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <in /> <ci> k </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Residue", "[", RowBox[List[RowBox[List["HarmonicNumber", "[", "z_", "]"]], ",", RowBox[List["{", RowBox[List["z_", ",", RowBox[List["-", "k_"]]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "1"]], "/;", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", ">", "0"]]]]]]]]]]


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





2001-10-29