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 HarmonicNumber

 http://functions.wolfram.com/06.16.09.0001.01

 Input Form

 HarmonicNumber[z] == Limit[Log[n] - Sum[1/(k + z + 1), {k, 0, n}], n -> Infinity] + EulerGamma

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HarmonicNumber", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List[RowBox[List["Log", "[", "n", "]"]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox["1", RowBox[List["k", "+", "z", "+", "1"]]]]]]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]], "+", "EulerGamma"]]]]]]

 MathML Form

 H HarmonicNumber z lim n "\[Rule]" ( log ( n ) - k = 0 n 1 k + z + 1 ) + TagBox["\[DoubledGamma]", Function[EulerGamma]] HarmonicNumber z n n n -1 k 0 n 1 k z 1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HarmonicNumber", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List[RowBox[List["Log", "[", "n", "]"]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox["1", RowBox[List["k", "+", "z", "+", "1"]]]]]]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]], "+", "EulerGamma"]]]]]]

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

 2001-10-29