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 HarmonicNumber

 http://functions.wolfram.com/06.16.06.0015.01

 Input Form

 HarmonicNumber[z] == z (1/(1 + z) + 1/(2 (2 + z)) + 1/(3 (3 + z)) + \[Ellipsis])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HarmonicNumber", "[", "z", "]"]], "\[Equal]", RowBox[List["z", " ", RowBox[List["(", RowBox[List[FractionBox["1", RowBox[List["1", "+", "z"]]], "+", FractionBox["1", RowBox[List["2", " ", RowBox[List["(", RowBox[List["2", "+", "z"]], ")"]]]]], "+", FractionBox["1", RowBox[List["3", " ", RowBox[List["(", RowBox[List["3", "+", "z"]], ")"]]]]], "+", "\[Ellipsis]"]], ")"]]]]]]]]

 MathML Form

 H HarmonicNumber z z ( 1 z + 1 + 1 2 ( z + 2 ) + 1 3 ( z + 3 ) + ) HarmonicNumber z z 1 z 1 -1 1 2 z 2 -1 1 3 z 3 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HarmonicNumber", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["z", " ", RowBox[List["(", RowBox[List[FractionBox["1", RowBox[List["1", "+", "z"]]], "+", FractionBox["1", RowBox[List["2", " ", RowBox[List["(", RowBox[List["2", "+", "z"]], ")"]]]]], "+", FractionBox["1", RowBox[List["3", " ", RowBox[List["(", RowBox[List["3", "+", "z"]], ")"]]]]], "+", "\[Ellipsis]"]], ")"]]]]]]]]

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

 2001-10-29

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